Managerial incentives to increase firm volatility provided by debt stock and options

Joshua D Anderson jdandersmitedu

(617) 253-7974

John E Core jcoremitedu (617) 715-4819

Abstract We measure a managerrsquos risk-taking incentives as the total sensitivity of the managerrsquos debt stock and option holdings to firm volatility We compare this measure to the option vega and to relative measures used by the prior literature Vega does not reflect the option value of equity does not capture risk incentives from managersrsquo stock and debt holdings and does not reflect the fact that employee options are warrants The relative measures do not incorporate the sensitivity of options to volatility The new measure explains risk choices better than vega and the relative measures Our measure should be useful for future research on managersrsquo risk choices

This draft February 2014

_______________ Corresponding author We gratefully acknowledge comments from Ana Albuquerque (discussant) Divya Anantharaman Wayne Guay Mitchell Petersen Eric So Daniel Taylor Anand Venkateswaran Jerry Zimmerman and seminar participants at the American Accounting Association 2012 Annual Meeting Columbia University MIT Sloan School of Management Northeastern University Pennsylvania State University Temple University Tulane University the University of Technology Sydney and Washington University at St Louis We thank Ingolf Dittmann for his estimates of CEO non-firm wealth We appreciate the financial support of the MIT Sloan School of Management

1

1 Introduction

A large literature uses the sensitivity of stock options to an increase in stock volatility

(ldquovegardquo) to study whether managersrsquo equity portfolios provide incentives to increase risk

Studies on early samples show a strong positive association between vega and risk-taking (Guay

1999 Coles et al 2006) whereas studies on later samples show mixed results (eg Hayes et al

2012) We re-examine vega and show that it has three shortcomings (1) it does not reflect the

option value of equity (2) it does not capture potential risk incentives from managersrsquo stock and

inside debt (unsecured pensions and deferred compensation) and (3) it does not reflect the fact

that employee options are warrants We derive and calculate an overall measure of a managerrsquos

risk-taking incentives using the total sensitivity of the managerrsquos debt stock and option holdings

to firm volatility

Limited liability implies that equity is an option on firm value with a strike price equal to

the face value of debt Consequently an increase in firm volatility increases equity value by

reducing debt value (Black and Scholes 1973 Merton 1974) When a firm has options this

increase in equity value is shared between the stock and options This implies that the option

sensitivity to volatility is larger than vega Because options are warrants an increase in volatility

that increases option value comes in part from a decrease in stock value If the firm has no debt

all of the increase in option value comes from a decrease in stock value This implies a stock

sensitivity to volatility that goes from being negative to positive as leverage increases A

managerrsquos attitude toward risk will be affected by the sensitivities of the managersrsquo holdings of

debt stock and options to firm volatility

To estimate these sensitivities we follow Merton (1974) and value total firm equity

(stock and stock options) as an option on the value of firm assets The model gives an estimate of

2

the decrease in debt value for an increase in firm volatility This decrease in debt value implies

an equal increase in equity value In turn the increase in equity value is shared between the stock

and stock options We estimate the CEOrsquos sensitivities by applying the CEOrsquos ownership of debt

stock and options to the firmrsquos sensitivities

We estimate these sensitivities for a sample of 5967 Execucomp CEO-years from 2006

to 2010 The typical CEO in our sample owns roughly 2 of the debt 2 of the stock and 16

of the options In terms of incentives to increase volatility this CEO has small negative

incentives from debt small positive incentives from stock and large positive incentives from

options A one standard deviation increase in firm volatility increases the average CEOrsquos wealth

by $3 million or 7 of total wealth

The total sensitivity increases as leverage increases but vega roughly remains constant

with leverage As leverage increases the debt sensitivity becomes more negative (making the

CEO averse to risk increases) but the equity sensitivity (the sum of stock and option sensitivities)

increases more rapidly This occurs because the stock sensitivity changes from being negative to

being strongly positive

Because vega does not capture these sensitivities it can be a noisy and biased measure of

risk-taking incentives If the total sensitivity better reflects CEO incentives we expect it to be

more highly associated with CEOsrsquo risk-taking choices To test this conjecture we examine the

association between the total sensitivity and vega and three proxies for future firm risk stock

volatility research and development expense and leverage We specify regression models

similar to those in Coles et al (2006) and Hayes et al (2012) Our results suggest that the total

sensitivity is more highly associated with risk-taking than is vega

3

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

scaled equity vega1

Our new measures require only data from CRSP Compustat and Execucomp The

measures can be computed for virtually all of the sample for which vega can be computed2 A

program to compute the measures is available on request

A concern about regressions of incentives on risk-taking is that risk-taking incentives are

endogenous To explore the robustness of our results we estimate two-stage least squares (2SLS)

regressions The inference from the 2SLS regressions is similar The total sensitivity measure

explains risk choices better than vega We also follow Hayes et al and examine changes in

incentives and in risk-taking around the introduction of option expensing in 2005 as a potentially

exogenous event that changed incentives Our evidence from this analysis also suggests that the

total sensitivity measure explains risk choices better than vega

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures (the relative leverage ratio and the relative incentive ratio) used in the 1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample 2 As described below to compute the total sensitivity requires data on outstanding employee stock options This data is missing from Compustat for about 4 of our main sample In addition in a small number of cases the algorithm to compute debt values does not converge which makes it impossible to compute our measure

4

recent literature (eg Cassell et al 2012 Sundaram and Yermack 2007 Wei and Yermack

2011) are noisy and can be biased These measures do not correctly incorporate the sensitivity of

option value to firm volatility We calculate a measure that correctly weights the managerrsquos debt

stock and option sensitivities The prior measures suggest that CEOs on average are highly

aligned with debt holders the average CEO has debt incentives to reduce volatility that are over

23 times his equity incentives to increase volatility By contrast the corrected measure which

explicitly takes into account the incentives to increase firm volatility from options is much

smaller and suggests that CEOs have little alignment with debt holders the average CEO has

incentives to reduce volatility that are equal to 04 times his equity incentives to increase

volatility Consistent with prior literature we find that these ratios are negatively associated with

risk choices However our scaled total sensitivity measure can be computed for about 70 more

observations and is more highly associated with risk-taking choices than the relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

5

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

6

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted So long as increases in

volatility do not change the value of the firm any gains to the options are offset by losses to the

stock This result for options on stock is similar to the result when stock is an option on the value

of the levered firm

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have a call option on the assets but they have

granted options on the equity to employees They are in a position with respect to the equity

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

1

1 Introduction

A large literature uses the sensitivity of stock options to an increase in stock volatility

(ldquovegardquo) to study whether managersrsquo equity portfolios provide incentives to increase risk

Studies on early samples show a strong positive association between vega and risk-taking (Guay

1999 Coles et al 2006) whereas studies on later samples show mixed results (eg Hayes et al

2012) We re-examine vega and show that it has three shortcomings (1) it does not reflect the

option value of equity (2) it does not capture potential risk incentives from managersrsquo stock and

inside debt (unsecured pensions and deferred compensation) and (3) it does not reflect the fact

that employee options are warrants We derive and calculate an overall measure of a managerrsquos

risk-taking incentives using the total sensitivity of the managerrsquos debt stock and option holdings

to firm volatility

Limited liability implies that equity is an option on firm value with a strike price equal to

the face value of debt Consequently an increase in firm volatility increases equity value by

reducing debt value (Black and Scholes 1973 Merton 1974) When a firm has options this

increase in equity value is shared between the stock and options This implies that the option

sensitivity to volatility is larger than vega Because options are warrants an increase in volatility

that increases option value comes in part from a decrease in stock value If the firm has no debt

all of the increase in option value comes from a decrease in stock value This implies a stock

sensitivity to volatility that goes from being negative to positive as leverage increases A

managerrsquos attitude toward risk will be affected by the sensitivities of the managersrsquo holdings of

debt stock and options to firm volatility

To estimate these sensitivities we follow Merton (1974) and value total firm equity

(stock and stock options) as an option on the value of firm assets The model gives an estimate of

2

the decrease in debt value for an increase in firm volatility This decrease in debt value implies

an equal increase in equity value In turn the increase in equity value is shared between the stock

and stock options We estimate the CEOrsquos sensitivities by applying the CEOrsquos ownership of debt

stock and options to the firmrsquos sensitivities

We estimate these sensitivities for a sample of 5967 Execucomp CEO-years from 2006

to 2010 The typical CEO in our sample owns roughly 2 of the debt 2 of the stock and 16

of the options In terms of incentives to increase volatility this CEO has small negative

incentives from debt small positive incentives from stock and large positive incentives from

options A one standard deviation increase in firm volatility increases the average CEOrsquos wealth

by $3 million or 7 of total wealth

The total sensitivity increases as leverage increases but vega roughly remains constant

with leverage As leverage increases the debt sensitivity becomes more negative (making the

CEO averse to risk increases) but the equity sensitivity (the sum of stock and option sensitivities)

increases more rapidly This occurs because the stock sensitivity changes from being negative to

being strongly positive

Because vega does not capture these sensitivities it can be a noisy and biased measure of

risk-taking incentives If the total sensitivity better reflects CEO incentives we expect it to be

more highly associated with CEOsrsquo risk-taking choices To test this conjecture we examine the

association between the total sensitivity and vega and three proxies for future firm risk stock

volatility research and development expense and leverage We specify regression models

similar to those in Coles et al (2006) and Hayes et al (2012) Our results suggest that the total

sensitivity is more highly associated with risk-taking than is vega

3

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

scaled equity vega1

Our new measures require only data from CRSP Compustat and Execucomp The

measures can be computed for virtually all of the sample for which vega can be computed2 A

program to compute the measures is available on request

A concern about regressions of incentives on risk-taking is that risk-taking incentives are

endogenous To explore the robustness of our results we estimate two-stage least squares (2SLS)

regressions The inference from the 2SLS regressions is similar The total sensitivity measure

explains risk choices better than vega We also follow Hayes et al and examine changes in

incentives and in risk-taking around the introduction of option expensing in 2005 as a potentially

exogenous event that changed incentives Our evidence from this analysis also suggests that the

total sensitivity measure explains risk choices better than vega

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures (the relative leverage ratio and the relative incentive ratio) used in the 1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample 2 As described below to compute the total sensitivity requires data on outstanding employee stock options This data is missing from Compustat for about 4 of our main sample In addition in a small number of cases the algorithm to compute debt values does not converge which makes it impossible to compute our measure

4

recent literature (eg Cassell et al 2012 Sundaram and Yermack 2007 Wei and Yermack

2011) are noisy and can be biased These measures do not correctly incorporate the sensitivity of

option value to firm volatility We calculate a measure that correctly weights the managerrsquos debt

stock and option sensitivities The prior measures suggest that CEOs on average are highly

aligned with debt holders the average CEO has debt incentives to reduce volatility that are over

23 times his equity incentives to increase volatility By contrast the corrected measure which

explicitly takes into account the incentives to increase firm volatility from options is much

smaller and suggests that CEOs have little alignment with debt holders the average CEO has

incentives to reduce volatility that are equal to 04 times his equity incentives to increase

volatility Consistent with prior literature we find that these ratios are negatively associated with

risk choices However our scaled total sensitivity measure can be computed for about 70 more

observations and is more highly associated with risk-taking choices than the relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

5

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

6

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted So long as increases in

volatility do not change the value of the firm any gains to the options are offset by losses to the

stock This result for options on stock is similar to the result when stock is an option on the value

of the levered firm

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have a call option on the assets but they have

granted options on the equity to employees They are in a position with respect to the equity

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

2

the decrease in debt value for an increase in firm volatility This decrease in debt value implies

an equal increase in equity value In turn the increase in equity value is shared between the stock

and stock options We estimate the CEOrsquos sensitivities by applying the CEOrsquos ownership of debt

stock and options to the firmrsquos sensitivities

We estimate these sensitivities for a sample of 5967 Execucomp CEO-years from 2006

to 2010 The typical CEO in our sample owns roughly 2 of the debt 2 of the stock and 16

of the options In terms of incentives to increase volatility this CEO has small negative

incentives from debt small positive incentives from stock and large positive incentives from

options A one standard deviation increase in firm volatility increases the average CEOrsquos wealth

by $3 million or 7 of total wealth

The total sensitivity increases as leverage increases but vega roughly remains constant

with leverage As leverage increases the debt sensitivity becomes more negative (making the

CEO averse to risk increases) but the equity sensitivity (the sum of stock and option sensitivities)

increases more rapidly This occurs because the stock sensitivity changes from being negative to

being strongly positive

Because vega does not capture these sensitivities it can be a noisy and biased measure of

risk-taking incentives If the total sensitivity better reflects CEO incentives we expect it to be

more highly associated with CEOsrsquo risk-taking choices To test this conjecture we examine the

association between the total sensitivity and vega and three proxies for future firm risk stock

volatility research and development expense and leverage We specify regression models

similar to those in Coles et al (2006) and Hayes et al (2012) Our results suggest that the total

sensitivity is more highly associated with risk-taking than is vega

3

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

scaled equity vega1

Our new measures require only data from CRSP Compustat and Execucomp The

measures can be computed for virtually all of the sample for which vega can be computed2 A

program to compute the measures is available on request

A concern about regressions of incentives on risk-taking is that risk-taking incentives are

endogenous To explore the robustness of our results we estimate two-stage least squares (2SLS)

regressions The inference from the 2SLS regressions is similar The total sensitivity measure

explains risk choices better than vega We also follow Hayes et al and examine changes in

incentives and in risk-taking around the introduction of option expensing in 2005 as a potentially

exogenous event that changed incentives Our evidence from this analysis also suggests that the

total sensitivity measure explains risk choices better than vega

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures (the relative leverage ratio and the relative incentive ratio) used in the 1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample 2 As described below to compute the total sensitivity requires data on outstanding employee stock options This data is missing from Compustat for about 4 of our main sample In addition in a small number of cases the algorithm to compute debt values does not converge which makes it impossible to compute our measure

4

recent literature (eg Cassell et al 2012 Sundaram and Yermack 2007 Wei and Yermack

2011) are noisy and can be biased These measures do not correctly incorporate the sensitivity of

option value to firm volatility We calculate a measure that correctly weights the managerrsquos debt

stock and option sensitivities The prior measures suggest that CEOs on average are highly

aligned with debt holders the average CEO has debt incentives to reduce volatility that are over

23 times his equity incentives to increase volatility By contrast the corrected measure which

explicitly takes into account the incentives to increase firm volatility from options is much

smaller and suggests that CEOs have little alignment with debt holders the average CEO has

incentives to reduce volatility that are equal to 04 times his equity incentives to increase

volatility Consistent with prior literature we find that these ratios are negatively associated with

risk choices However our scaled total sensitivity measure can be computed for about 70 more

observations and is more highly associated with risk-taking choices than the relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

5

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

6

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted So long as increases in

volatility do not change the value of the firm any gains to the options are offset by losses to the

stock This result for options on stock is similar to the result when stock is an option on the value

of the levered firm

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have a call option on the assets but they have

granted options on the equity to employees They are in a position with respect to the equity

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

3

The total sensitivity measure requires data on CEOsrsquo inside debt which data became

available only in 2006 To avoid this limitation we also examine the equity sensitivity which is

equal to the sum of the stock sensitivity and the option sensitivity (or the total sensitivity minus

the debt sensitivity) The equity sensitivity is very highly correlated with the total sensitivity

because the debt sensitivity is small and has low variance We compute the equity sensitivity

from 1994-2005 and compare it with vega In this sample we also find that equity sensitivity

explains risk-taking better than vega and that the scaled equity sensitivity is superior to the

scaled equity vega1

Our new measures require only data from CRSP Compustat and Execucomp The

measures can be computed for virtually all of the sample for which vega can be computed2 A

program to compute the measures is available on request

A concern about regressions of incentives on risk-taking is that risk-taking incentives are

endogenous To explore the robustness of our results we estimate two-stage least squares (2SLS)

regressions The inference from the 2SLS regressions is similar The total sensitivity measure

explains risk choices better than vega We also follow Hayes et al and examine changes in

incentives and in risk-taking around the introduction of option expensing in 2005 as a potentially

exogenous event that changed incentives Our evidence from this analysis also suggests that the

total sensitivity measure explains risk choices better than vega

Our derivation of the sensitivity of debt stock and options also implies that the relative

risk-taking measures (the relative leverage ratio and the relative incentive ratio) used in the 1 Our finding that the equity sensitivity is superior to vega suggests that the stock sensitivity provides important incentives Guay (1999) also examines the stock sensitivity but finds that it does not have a large effect on incentives Potential reasons for the difference in our findings include (1) we value options as warrants (2) we use a different asset volatility calculation and (3) we use a different sample 2 As described below to compute the total sensitivity requires data on outstanding employee stock options This data is missing from Compustat for about 4 of our main sample In addition in a small number of cases the algorithm to compute debt values does not converge which makes it impossible to compute our measure

4

recent literature (eg Cassell et al 2012 Sundaram and Yermack 2007 Wei and Yermack

2011) are noisy and can be biased These measures do not correctly incorporate the sensitivity of

option value to firm volatility We calculate a measure that correctly weights the managerrsquos debt

stock and option sensitivities The prior measures suggest that CEOs on average are highly

aligned with debt holders the average CEO has debt incentives to reduce volatility that are over

23 times his equity incentives to increase volatility By contrast the corrected measure which

explicitly takes into account the incentives to increase firm volatility from options is much

smaller and suggests that CEOs have little alignment with debt holders the average CEO has

incentives to reduce volatility that are equal to 04 times his equity incentives to increase

volatility Consistent with prior literature we find that these ratios are negatively associated with

risk choices However our scaled total sensitivity measure can be computed for about 70 more

observations and is more highly associated with risk-taking choices than the relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

5

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

6

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted So long as increases in

volatility do not change the value of the firm any gains to the options are offset by losses to the

stock This result for options on stock is similar to the result when stock is an option on the value

of the levered firm

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have a call option on the assets but they have

granted options on the equity to employees They are in a position with respect to the equity

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

4

recent literature (eg Cassell et al 2012 Sundaram and Yermack 2007 Wei and Yermack

2011) are noisy and can be biased These measures do not correctly incorporate the sensitivity of

option value to firm volatility We calculate a measure that correctly weights the managerrsquos debt

stock and option sensitivities The prior measures suggest that CEOs on average are highly

aligned with debt holders the average CEO has debt incentives to reduce volatility that are over

23 times his equity incentives to increase volatility By contrast the corrected measure which

explicitly takes into account the incentives to increase firm volatility from options is much

smaller and suggests that CEOs have little alignment with debt holders the average CEO has

incentives to reduce volatility that are equal to 04 times his equity incentives to increase

volatility Consistent with prior literature we find that these ratios are negatively associated with

risk choices However our scaled total sensitivity measure can be computed for about 70 more

observations and is more highly associated with risk-taking choices than the relative ratios

We contribute to the literature in several ways We calculate a measure of risk-taking

incentives that includes the sensitivity of managersrsquo debt and stock holdings In addition our

measure better calculates the sensitivity of the managerrsquos stock options to firm volatility We

compare this measure to vega and to the relative measures used by the prior literature We find

that the new measure is more highly associated with risk choices than vega and the relative

measures Our measure should be useful for future research on managersrsquo risk choices

The remainder of the paper proceeds as follows In the next section we define the

sensitivity of firm debt stock and options to firm volatility We then define the corresponding

measures of the sensitivity of the CEOrsquos portfolio to firm volatility In the third section we

describe how we select a sample of CEOs and compare various measures of incentives In the

5

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

6

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted So long as increases in

volatility do not change the value of the firm any gains to the options are offset by losses to the

stock This result for options on stock is similar to the result when stock is an option on the value

of the levered firm

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have a call option on the assets but they have

granted options on the equity to employees They are in a position with respect to the equity

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

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Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

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volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

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values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

5

fourth section we compare regressions using the measures to explain various firm outcomes and

provide robustness tests In the fifth section we conclude

2 Definition of incentive measures

In this section we first show how firm debt equity and option values change with

changes in firm volatility and then we relate these changes to measures of managerial incentives

21 Sensitivity of firm capital structure to firm volatility

In general firms are financed with debt equity and employee options

(1)

Debt is the market value of the debt Stock is the market value of stock and Options is the

market value of options It is convenient to express stock and option values in per share amounts

and we assume the firm has n shares of stock outstanding with stock price P The firm has qn

stock options outstanding with option price W For simplicity in our notation we assume for the

moment that all options have the same exercise price and time to maturity so that each option is

worth W

To begin suppose that there are no stock options outstanding so that (1) becomes

(2)

Black and Scholes (1973) and Merton (1973) show that equity can be valued as a call with a

strike price equal to the face value of debt Under the assumption that changes in firm volatility

do not change the value of the firm

0 (3)

Therefore any loss in debt value due to volatility increases is offset by an equal gain in equity

value

6

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted So long as increases in

volatility do not change the value of the firm any gains to the options are offset by losses to the

stock This result for options on stock is similar to the result when stock is an option on the value

of the levered firm

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have a call option on the assets but they have

granted options on the equity to employees They are in a position with respect to the equity

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

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Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

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misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

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654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

6

(4)

More volatile returns increase the value of equity holdersrsquo call option which reduces the value of

debt The interests of debt and equity conflict Equity prefers higher firm volatility which raises

the value of its call debt prefers lower firm volatility which increases the value of its short call

Now consider a firm with no debt financed with stock and employee stock options

(5)

Employee stock options are warrants (W) because exercising the options results in the firm

issuing new shares of stock and receiving the strike price Analogous to (4) an increase in firm

volatility has the following effect on the stock price and the option price

(6)

Equation (6) shows that the price of a share of stock in a firm with only stock and employee

stock options decreases when firm volatility increases (Galai and Schneller 1978) The share

price decreases because the increased volatility makes it more likely that the option will be in the

money and that the current value of a share outstanding will be diluted So long as increases in

volatility do not change the value of the firm any gains to the options are offset by losses to the

stock This result for options on stock is similar to the result when stock is an option on the value

of the levered firm

Now we combine the results for debt and options An increase in firm volatility affects

debt stock and option value according to the following relation

(7)

In firms with both debt and options shareholders have a call option on the assets but they have

granted options on the equity to employees They are in a position with respect to the equity

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

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Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

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issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

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Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

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for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

7

similar to the position of the debt holders with respect to the assets When the firm is levered

increasing firm volatility causes shareholders to gain from the option on the asset but to lose on

the options on the equity Since the change in stockholdersrsquo value is a combination of these two

opposing effects whether stockholders prefer more volatility depends on the number of

employee options outstanding and firm leverage as we illustrate next

211 Estimating firm sensitivities

To estimate the sensitivities described above we calculate the value of debt and options

using standard pricing models We then increase firm volatility by 1 hold firm value fixed and

recalculate the values of debt stock and options We estimate the sensitivities to a one percent

change in firm volatility as the difference between these values Appendix A describes the details

and as noted above a program to compute the measures is available on request

We first price employee options as warrants using the Black-Scholes model as modified

to account for dividend payouts by Merton (1973) and modified to reflect warrant pricing by

Schulz and Trautmann (1994) Calculating option value this way gives a value for total firm

equity Second we model firm equity as an option on the levered firm following Merton (1974)

using the Black-Scholes formula This model allows us to calculate total firm value and firm

volatility following the approach of Eberhart (2005) With these values in hand we calculate the

value of the debt as a put on the firmrsquos assets with strike price equal to the maturity amount of

the firmrsquos debt3

3 Eberhart (2005) converts the firmrsquos debt into a single zero-coupon bond (as do Bharath and Shumway 2008 Campbell et al 2008 and Hillegeist et al 2004) In following this method we abstract away from different types of debt in the firmrsquos capital structure and different types of debt in the CEOrsquos portfolio Although doing this involves some measurement error it affords us a larger sample (in part because we do not require data on individual debt issues) and allows us to focus on the main effect equity values increase more after an increase in firm volatility when the firm has more debt

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

8

To calculate the sensitivities we increase firm volatility by 1 which implies a 1

increase in stock volatility We use this new firm volatility to determine a new debt value The

sensitivity of the debt to a change in firm volatility is the difference between this value and the

value at the lower firm volatility From (7) equity increases by the magnitude of the decrease in

the debt value Finally we use the higher equity value and higher stock volatility to compute a

new value for stock and stock options following Schulz and Trautmann (1994) The difference

between these stock and option values and those calculated in the first step is the sensitivity to

firm volatility for the stock and options

212 Example of firm sensitivities

To give intuition for the foregoing relations in Panel A of Table 1 we show the

sensitivities for an example firm We use values that are approximately the median values of our

sample described below The market value of assets is $25 billion and firm volatility is 35

Options are 7 of shares outstanding and have a price-to-strike ratio of 135 The options and

the debt have a maturity of four years Leverage is the face value of debt divided by the sum of

the book value of debt and market value of equity To calculate the values and sensitivities we

assume a risk-free rate of 225 that the interest rate on debt is equal to the risk-free rate and

that the firm pays no dividends

The first set of rows shows the change in the value of firm debt stock and options for a

1 increase in the standard deviation of the assets (from 3500 to 3535) at various levels of

leverage An increase in volatility reduces debt value and this reduction is greater for greater

leverage The reduction in debt value is shared between the stock and options Options always

benefit from increases in volatility When leverage is low the sensitivity of debt to firm volatility

is very low Since there is little debt to transfer value from option holders gain at the expense of

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

9

stockholders when volatility increases As leverage increases the sensitivity of debt to firm

volatility decreases As this happens the stock sensitivity becomes positive as the stock offsets

losses to options with gains against the debt

22 Managersrsquo incentives from the sensitivity of firm capital structure to firm volatility

221 Total incentives to increase firm volatility

We now use the above results to derive measures of managerial incentives A managerrsquos

(risk-neutral) incentives to increase volatility from a given security are equal to the securityrsquos

sensitivity to firm volatility multiplied by the fraction owned by the manager If the manager

owns α of the outstanding stock β of the outstanding debt and options the managerrsquos total

incentives to increase firm volatility are

(8)

where is the managerrsquos average per option sensitivity to firm volatility computed to reflect

that employee options are warrants

222 Vega incentives to increase stock volatility

Prior literature uses vega the sensitivity of managersrsquo option holdings to a change in

stock volatility as a proxy for incentives to increase volatility (Guay 1999 Core and Guay

2002 Coles et al 2006 Hayes et al 2012) Vega is the change in the Black-Scholes option

value for a change in stock volatility

(9)

(Here we use the notation O to indicate that the option is valued using Black-Scholes in contrast

to the notation W to indicate that the option is valued as a warrant) Comparing vega with the

total sensitivity in (8) one can see that vega is a subset of total risk-taking incentives In

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

10

particular it does not reflect the option value of equity does not include incentives from debt

and stock and does not account for the fact that employee stock options are warrants Inspection

of the difference between (8) and (9) reveals that for vega to be similar to total risk-taking

incentives the firm must have low or no leverage (so that the volatility increase causes little re-

distribution from debt value to equity value) and the firm must have low amounts of options (so

that the volatility increase causes little re-distribution from stock value to option value)

223 Relative incentives to increase volatility

Jensen and Meckling (1976) suggest a scaled measure of incentives the ratio of risk-

reducing incentives to risk-increasing incentives The ratio of risk-reducing to risk-increasing

incentives in (8) is equal to the ratio of debt incentives (multiplied by -1) to stock and option

incentives

4 (10)

We term this ratio the ldquorelative sensitivity ratiordquo As in Jensen and Meckling the ratio is

informative about whether the manager has net incentives to increase or decrease firm risk It can

be useful to know whether risk-reducing incentives are greater than risk-increasing incentives

(that is whether Eq (8) is negative or positive or equivalently whether the ratio in Eq (10) is

greater or less than one) If the ratio in Eq (10) is less than one then the manager has more risk-

increasing incentives than risk-reducing incentives and vice versa if the ratio is greater than one

When the managerrsquos portfolio of debt stock and options mirrors the firmrsquos capital structure the

ratio in (10) is one Jensen and Meckling (1976) posit that a manager with such a portfolio

4 From Panel A of Table 1 the sensitivity of stock to volatility can be negative when the firm has options but little

leverage In this case the ratio of risk-reducing to risk-increasing incentives is

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

11

ldquowould have no incentives whatsoever to reallocate wealthrdquo between capital providers (p 352)

by increasing the risk of the underlying assets

If the firm has no employee options the stock sensitivity is always positive and the

relative sensitivity ratio (10) becomes5

(11)

An advantage of this ratio is that if in fact the firm has no employee options one does not have

to estimate the sensitivity of debt to volatility to compute the ratio Much prior literature (eg

Cassell et al 2012 Sundaram and Yermack 2007) uses this measure and terms it the ldquorelative

leverage ratiordquo as it compares the managerrsquos leverage to the firmrsquos leverage To operationalize

the relative leverage ratio when firms have employee options these researchers make an ad hoc

adjustment by adding the Black-Scholes value of the options to the value of the firmrsquos stock and

CEOrsquos stock Alternatively Wei and Yermack (2011) make a different ad hoc adjustment for

options by converting the options into equivalent units of stock by multiplying the options by

their Black-Scholes delta These adjustments for options are not correct because the option

sensitivity to firm volatility is different from option value or delta Only when the firm has no

employee options are the relative leverage and incentive ratios equal to the relative sensitivity

ratio

More important scaling away the levels information contained in (8) can lead to incorrect

inference even when calculated correctly For example imagine two CEOs who both have $1

million total wealth and both have a relative sensitivity ratio of 09 Although they are otherwise

5 The first expression follows from (4) and the sensitivity of total debt value to volatility divides off

The second equality follows from the definition of β and α as the managerrsquos fractional holdings of debt and stock and re-arranging

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

12

identical CEO A has risk-reducing incentives of -$900 and has risk-increasing incentives of

$1000 while CEO B has risk-reducing incentives of -$90000 and has risk-increasing incentives

of $100000 The relative measure (09) scales away the sensitivities and suggests that both

CEOs make the same risk choices However CEO B is much more likely to take risks his

wealth increases by $10000 (1 of wealth) for each 1 increase in firm volatility while CEO

Arsquos increases by only $100 (001 of wealth)

224 Empirical estimation of CEO sensitivities

We calculate CEO sensitivities as weighted functions of the firm sensitivities The CEOrsquos

debt and stock sensitivities are the CEOrsquos percentage ownership of debt and stock multiplied by

the firm sensitivities We calculate the average strike price and maturity of the managerrsquos options

following Core and Guay (2002) We calculate the value of the CEOrsquos options following Schulz

and Trautmann (1994) Appendix A5 provides details and notes the necessary Execucomp

Compustat and CRSP variable names

Calculating the sensitivities requires a normalization for the partial derivatives

Throughout this paper we report results using a 1 increase in firm volatility which is

equivalent to a 1 increase in stock volatility In other words to calculate a sensitivity we first

calculate a value using current volatility then increase volatility by 1 101 and re-

calculate the value The sensitivity is the difference in these values Prior literature (eg Guay

1999) calculates vega using a 001 increase in stock volatility The disadvantage of using a 001

increase in stock volatility in calculating vega is that it implies an increase in firm volatility that

grows smaller than 001 as firm leverage increases So that the measures are directly comparable

we therefore use a 1 increase in stock volatility to compute vega The 1 vega is highly

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

13

correlated (091) with the 001 increase vega used in the prior literature and all of our inferences

below with the 1 vega are identical to those with the 001 increase vega6

225 Example of CEO sensitivities

In Panel B of Table 1 we illustrate how incentives to take risk vary with firm leverage

for an example CEO (of the example firm introduced above) The example CEO owns 2 of the

firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options These percentages are similar

to the averages for our main sample described below

Columns (2) to (4) show the sensitivities of the CEOrsquos debt stock and options to a 1

change in firm volatility for various levels of leverage As with the firm sensitivities the

example CEOrsquos debt sensitivity decreases monotonically with leverage while the sensitivities of

stock and options increase monotonically with leverage Column (5) shows that the total equity

sensitivity which is the sum of the stock and option sensitivities increases sharply as the stock

sensitivity goes from being negative to positive Column (6) shows the total sensitivity which is

the sum of the debt stock and option sensitivities These total risk-taking incentives increase

monotonically with leverage as the decrease in the debt sensitivity is outweighed by the increase

in the equity sensitivity

Column (7) shows vega for the example CEO In contrast to the equity sensitivity and the

total sensitivity which both increase in leverage vega first increases and then decreases with

leverage in this example Part of the reason is that vega does not capture the debt and stock

sensitivities Holding this aside vega does not measure well the sensitivity of the option to firm

volatility It captures the fact that the option price is sensitive to stock volatility but it misses the

fact that equity value benefits from decreases in debt value As leverage increases the sensitivity

6 We also compute the change in the CEOrsquos wealth for a one sample standard deviation increase in firm volatility The results in terms of significance are very similar to our main results

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

14

of stock price to firm volatility increases dramatically (as shown by the increasingly negative

debt sensitivity) but this effect is omitted from the vega calculations

Columns (8) to (10) illustrate the various relative incentive measures The relative

sensitivity measure in Column (8) is calculated following Eq (10) as the negative of the sum of

debt and stock sensitivities divided by the option sensitivity when the stock sensitivity is

negative (as for the three lower leverage values) and as the negative of debt sensitivity divided

by the sum of the stock and option sensitivity otherwise Thus risk-reducing incentives are $6

thousand for the low-leverage firms and $57 thousand for the high-leverage firms The risk-

increasing incentives are $46 for the low-leverage firms and $115 for the high-leverage firms

Accordingly as leverage increases the relative sensitivity measure increases from 013 (= 646)

to 050 (= 57115) indicating that the CEO is more identified with debt holders (has fewer

relative risk-taking incentives) This inference that risk-taking incentives decline is the opposite

of the increase in risk-taking incentives shown in Column (6) for the total sensitivity and total

sensitivity as a percentage of total wealth This example illustrates the point above that scaling

away the levels information contained in Eq (8) can lead to incorrect inference even when the

relative ratio is calculated correctly

In columns (9) and (10) we illustrate the relative leverage and relative incentive ratios

for our example CEO The relative leverage ratio is computed by dividing the CEOrsquos percentage

debt ownership (2) by the CEOrsquos ownership of total stock and option value (roughly 24)

Because these value ratios do not change much with leverage the relative leverage ratio stays

about 08 suggesting that the CEO is highly identified with debt holders The relative incentive

ratio which is similarly computed by dividing the CEOrsquos percentage debt ownership (2) by the

CEOrsquos ownership of total stock and option delta (roughly 28) also shows high identification

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

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Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

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misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

15

with debt holders and little change with leverage Again this is inconsistent with the substantial

increase in risk-taking incentives illustrated in Column (6) for the total sensitivity

3 Sample and Variable Construction

31 Sample Selection

We use two samples of Execucomp CEO data Our main sample contains Execucomp

CEOs from 2006 to 2010 and our secondary sample described in more detail in Section 44

below contains Execucomp CEOs from 1994 to 2005

The total incentive measures described above require information on CEO inside debt

(pensions and deferred compensation) and on firm options outstanding Execucomp provides

information on inside debt beginning only in 2006 (when the SEC began to require detailed

disclosures) Our main sample therefore begins in 2006 The sample ends in 2010 because our

tests require one-year ahead data that is only available through 2011 Following Coles et al

(2006) and Hayes et al (2012) we remove financial firms (firms with SIC codes between 6000

and 6999) and utility firms (firms with SIC codes between 4900 and 4999) We identify an

executive as CEO if we can calculate CEO tenure from Execucomp data and if the CEO is in

office at the end of the year If the firm has more than one CEO during the year we choose the

individual with the higher total pay We merge the Execucomp data with data from Compustat

and CRSP The resulting sample contains 5967 CEO-year observations that have complete data

32 Descriptive statistics ndash firm size volatility and leverage

Table 2 shows descriptive statistics for volatility the market value of firm debt stock

and options and leverage for the firms in our sample We describe in Appendix A3 how we

estimate firm market values following Eberhart (2005) To mitigate the effect of outliers we

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

16

winsorize all variables each year at the 1st and 99th percentiles Because our sample consists of

SampP 1500 firms the firms are large and have moderate volatility Most firms in the sample have

low leverage The median value of leverage is 13 and the mean is 18 These low amounts of

leverage suggest low agency costs of asset substitution for most sample firms (Jensen and

Meckling 1976)

33 Descriptive statistics ndash CEO incentive measures

Table 3 Panel A shows full sample descriptive statistics for the CEO incentive measures

We detail in Appendix A how we calculate these sensitivities As with the firm variables

described above we winsorize all incentive variables each year at the 1st and 99th percentiles7

The average CEO in our sample has some incentives from debt to decrease risk but the

amount of these incentives is low This is consistent with low leverage in the typical sample firm

Nearly half of the CEOs have no debt incentives The magnitude of the incentives from stock to

increase firm risk is also small for most managers but there is substantial variation in these

incentives with a standard deviation of approximately $47 thousand as compared to $16

thousand for debt incentives The average sensitivity of the CEOrsquos options to firm volatility is

much larger The mean value of the total (debt stock and option) sensitivity is $65 thousand

which indicates that a 1 increase in firm volatility provides the average CEO in our sample

with $65 thousand in additional wealth Vega is smaller than the total sensitivity and has strictly

positive values as compared to the total sensitivity which has about 8 negative values8

While the level measures of the CEOrsquos incentives are useful they are difficult to interpret

in cross-sectional comparisons of CEOs who have different amounts of wealth Wealthier CEOs

7 Consequently the averages in the table do not add ie the average total sensitivity is not equal the sum of the average debt sensitivity and average equity sensitivity 8 As discussed above this vega is calculated for a 1 increase in stock volatility rather than the 001 increase used in prior literature to make it comparable to the total sensitivity

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

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Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

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Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

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654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

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and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

17

will respond less to the same dollar amount of incentives if wealthier CEOs are less risk-averse9

In this case a direct way to generate a measure of the strength of incentives across CEOs is to

scale the level of incentives by the CEOrsquos wealth We estimate CEO total wealth as the sum of

the value of the CEOrsquos debt stock and option portfolio and wealth outside the firm10 We use

the measure of CEO outside wealth developed by Dittmann and Maug (2007)1112 The average

scaled total sensitivity is 014 of wealth The value is low because the sensitivities are

calculated with respect to a 1 increase in firm volatility If the average CEO increases firm

volatility by one standard deviation (199) that CEOrsquos wealth increases by 7 While some

CEOs have net incentives to decrease risk these incentives are small For the CEO at the first

percentile of the distribution who has relatively large risk-reducing incentives a one standard

deviation decrease in firm volatility increases the CEOrsquos wealth by 2

34 Descriptive statistics ndash CEO relative incentive measures

Panel A shows that the mean (median) relative leverage ratio is 309 (018) and the mean

(median) relative incentive ratio is 231 (015) These values are similar to those in Cassell et al

(2012) who also use an Execucomp sample These ratios are skewed and are approximately one

at the third quartile suggesting that 25 of our sample CEOs have incentives to decrease risk

This fraction is much larger than the 8 of CEOs with net incentives to reduce risk based on the

9 It is frequently assumed in the literature (eg Hall and Murphy 2002 Lewellen 2006 Conyon et al 2011) that CEOs have decreasing absolute risk aversion 10 We value the options as warrants following Schulz and Trautmann (1994) This is consistent with how we calculate the sensitivities of the CEOsrsquo portfolios 11 To develop the proxy Dittmann and Maug assume that the CEO enters the Execucomp database with no wealth and then accumulates outside wealth from cash compensation and selling shares Dittmann and Maug assume that the CEO does not consume any of his outside wealth The only reduction in outside wealth comes from using cash to exercise his stock options and paying US federal taxes Dittmann and Maug claim that their proxy is the best available given that managersrsquo preferences for saving and consumption are unobservable We follow Dittmann and Maug (2007) and set negative estimates of outside wealth to missing 12 The wealth proxy is missing for approximately 13 of CEOs For those CEOs we impute outside wealth using a model that predicts outside wealth as a function of CEO and firm characteristics If we instead discard observations with missing wealth our inference below is the same

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

18

total sensitivity measure and suggests a bias in the relative leverage and incentive measures By

contrast the mean (median) relative sensitivity ratio is 042 (003) suggesting low incentives to

decrease risk

35 Correlations ndash CEO incentive measures

Panel B of Table 3 shows Pearson correlations between the incentive measures Focusing

first on the levels the total sensitivity and vega are highly correlated (069) The total sensitivity

is almost perfectly correlated with the equity sensitivity (099) Since CEOsrsquo inside debt

sensitivity to firm volatility has a low variance including debt sensitivity does not provide much

incremental information about CEOsrsquo incentives The scaled total sensitivity and scaled vega are

also highly correlated (079) and the scaled total sensitivity is almost perfectly correlated with

the scaled equity sensitivity (098) The relative leverage and relative incentive ratios are almost

perfectly correlated (099) Because the correlation is so high we do not include the relative

incentive ratio in our subsequent analyses

4 Associations of incentive measures with firm risk choices

41 Research Design

411 Unscaled incentive measures

We examine how the CEOrsquos incentives at time t are related to firm risk choices at time

t+1 using regressions of the following form

Firm Risk Choice Risk-taking Incentives Delta sum Control (12)

The form of the regression is similar to those in Guay (1999) Coles et al (2006) and Hayes et al

(2012)

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

19

Guay (1999 p 46) shows that managerrsquos incentives to increase risk are positively related

to the sensitivity of wealth to volatility but negatively related to the increase in the managerrsquos

risk premium that occurs when firm risk increases Prior researchers examining vega (eg

Armstrong et al 2013 p 330) argue that ldquovega provides managers with an unambiguous

incentive to adopt risky projectsrdquo and that this relation should manifest empirically so long as

the regression adequately controls for differences in the risk premiums Delta (incentives to

increase stock price) is an important determinant of the managerrsquos risk premium When a

managerrsquos wealth is more concentrated in firm stock he is less diversified and requires a greater

risk premium when firm risk increases We control for the delta of the CEOrsquos equity portfolio

measured following Core and Guay (2002) To ease comparisons we use this delta in all of our

regressions13

Finally we also control for cash compensation and CEO tenure which prior literature

(Guay 1999 Coles et al 2006) uses as proxies for the CEOrsquos outside wealth and risk aversion

We use three proxies for firm risk choices (1) ln(Stock Volatility) measured using daily

stock volatility over year t+1 (2) RampD Expense measured as the ratio of RampD expense to total

assets and (3) Book Leverage measured as the book value of long-term debt to the book value of

assets14 Like the prior literature we consider ln(Stock Volatility) to be a summary measure of

the outcome of firm risk choices RampD Expense to be a major input to increased risk through

investment risk and Book Leverage to be a major input to increased risk through capital structure

13 Our arguments above -- that an increase in equity value will be split between stock and option holders -- suggest that delta as calculated in the prior literature can also be noisy We calculate a dilution-adjusted delta by estimating the increase in the value of the CEOrsquos stock and option portfolio when the firmrsquos equity value increases by 1 If we instead use this dilution-adjusted delta in our tests the results using this delta are very similar to those presented below 14 We also examine the relation between our incentive measures and asset volatility and idiosyncratic volatility below

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

20

risk We measure all control variables at t and all risk choice variables at t+1 By doing this we

attempt to mitigate potential endogeneity

Other control variables in these regressions follow Coles et al (2006) and Hayes et al

(2012) We control for firm size using ln(Sales) and for growth opportunities using Market-to-

Book All our regressions include year and 2-digit SIC industry fixed effects

In the regression with ln(Stock Volatility) we also control for risk from past RampD

Expense CAPEX and Book Leverage In the regression with RampD Expense we also control for

ln(Sales Growth) and Surplus Cash In the regression with Book Leverage as the dependent

variable we control for ROA and follow Hayes et al (2012) by controlling for PPE the quartile

rank of a modified version of the Altman (1968) Z-score and whether the firm has a long-term

issuer credit rating

Following Hayes et al (2012) we use nominal values that are not adjusted for inflation

and estimate our regressions using OLS If we follow Coles et al (2006) and adjust for inflation

our inference is the same Coles et al also present the results of instrumental variables

regressions We report our main results using ordinary least squares In section 451 below we

examine the sensitivity of our results using two-stage least-squares (2SLS) and find similar

inference

412 Scaled incentive measures

Prior literature identifies CEO wealth as an important determinant of a CEOrsquos attitude

toward risk As noted above the larger delta is relative to wealth the greater the risk premium

the CEO demands Likewise the larger risk-taking incentives are relative to wealth the more a

given risk increase will change the CEOrsquos wealth and the greater the CEOrsquos motivation to

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

21

increase risk To capture these effects more directly we scale risk-taking incentives and delta by

wealth and control for wealth in the following alternative specification

Firm Risk Choice

Risk-taking IncentivesWealth DeltaWealth + Wealth +sum Control

(13)

To enable comparison across the models we include the same control variables in (13) as in (12)

above

42 Association of level and scaled incentive measures with firm risk choices

In Table 4 we present our main results Panel A contains estimation results for the

unscaled incentive variables (Eq (12)) and Panel B contains estimation results for the scaled

incentive variables (Eq (13)) Each panel contains three columns for vega (scaled vega) and

three columns for total sensitivity (scaled total sensitivity) Each set of columns shows regression

results for ln(Stock Volatility) RampD Expense and Book Leverage

Vega has unexpected significant negative coefficients in the model for ln(Stock Volatility)

in Column (1) of Panel A and for leverage in Column (3) These results are inconsistent with

findings in Coles at al (2006) for 1992-200115 This finding and findings in Hayes et al (2012)

are consistent with changes in the cross-sectional relation between vega and risk-taking over

time In column (2) however vega has the expected positive and significant relation with RampD

Expense

To ease interpretation of our variables we standardize each dependent and independent

variable (by subtracting its mean and dividing by its standard deviation) so that that the variables

have a mean of zero and standard deviation of one This transformation does not affect the t- 15 In Section 44 below we examine 1994-2005 data During this time period that is more comparable to Coles et al (2006) we find a positive association between vega and ln(Stock Volatility)

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

22

statistic but helps with interpretation For example the 0151 coefficient on vega in Column (2)

indicates that a one standard deviation increase in vega is associated with a 0151 standard

deviation increase in RampD Expense

At the bottom of the panel the average coefficient on vega (0008) is not significantly

greater than zero suggesting that overall vega is not significantly associated with these three risk

choices In contrast the total sensitivity is positive in all three specifications and significant in

the models for RampD Expense and Book Leverage16 The average coefficient on total sensitivity

(0077) is significantly greater than zero and is significantly greater than the average coefficient

on vega This result suggests that for this sample total sensitivity better explains risk choices than

vega

As noted above scaling the level of incentives by total wealth can provide a better cross-

sectional measure of CEOsrsquo incentives In Panel B the scaled vega is positive in all three

specifications and significant in the models for RampD Expense and Book Leverage The sum of

the three coefficients on scaled vega is significantly greater than zero The scaled total sensitivity

is both positively and significantly related to all three risk variables The average coefficient on

both scaled vega and scaled sensitivity are significantly greater than zero suggesting that both

variables explain risk choices However the average coefficient on scaled sensitivity (0231) is

16 We note that the total sensitivity is a noisy measure of incentives to increase leverage An increase in leverage does not affect asset volatility but does increase stock volatility The total sensitivity therefore is only correlated with a leverage increase through components sensitive to stock volatility (options and the warrant effect of options on stock) but not through components sensitive to asset volatility (debt and the debt effect on equity)Similar to Lewellen (2006) we also calculate a direct measure of the sensitivity of the managerrsquos portfolio to a leverage increase To do this we assume that leverage increases because 1 of the asset value is used to repurchase equity The firm repurchases shares and options pro rata so that option holders and shareholders benefit equally from the repurchase The CEO does not sell stock or options The sensitivity of the managerrsquos portfolio to the increase in leverage has a 067 correlation with the total sensitivity The sensitivity to increases in leverage has a significantly higher association with book leverage than the total sensitivity However there is not a significant difference in the association when both measures are scaled by wealth

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

23

significantly greater than the average coefficient on scaled vega (0131) suggesting that scaled

sensitivity explains risk choices better

Overall the results in Table 4 suggest that the total sensitivity explains firmsrsquo risk

choices better than vega

In Columns (1) and (2) of Table 5 we show robustness to using asset volatility as the

dependent variable instead of stock volatility For parsimony and because our main interest is

risk-taking incentives in the remainder of the paper we tabulate only the risk-taking incentive

variables Panel A shows that vega and total sensitivity are significantly related to asset volatility

While the coefficient on total sensitivity is 19 larger than that on vega the difference is not

significant In Panel B both scaled incentive variables are significantly related to asset volatility

Scaled total sensitivity has a 14 larger effect on asset volatility than scaled vega but this

difference is not significant

In the remaining columns we decompose stock volatility into its systematic and

idiosyncratic components by regressing daily returns on the Fama and French (1993) factors

Columns (3) through (6) of Table 5 show the regressions using the components of stock

volatility as the dependent variables In Panel A vega has a significantly negative relation with

both systematic and idiosyncratic volatility Total sensitivity has a positive but insignificant

relation with both components In Panel B scaled vega has an insignificant positive relation with

both systematic and idiosyncratic volatility In contrast scaled total sensitivity has a significant

positive relation with both systematic and idiosyncratic volatility Scaled total sensitivity has a

significantly larger association with both components of volatility than does scaled vega

43 Association of relative ratios with firm risk choices

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

24

The preceding section compares the total sensitivity to vega In this section and in Table

6 we compare the scaled total sensitivity to the relative leverage ratio 17 The regression

specifications are identical to Table 4 These specifications are similar to but not identical to

those of Cassell et al (2012)18

The relative leverage ratio has two shortcomings as a regressor First it is not defined for

firms with no debt or for CEOs with no equity incentives so our largest sample in Table 6 is

4994 firm-years as opposed to 5967 in Table 4 Second as noted above and in Cassell et al

(2012) when the CEOsrsquo inside debt is large relative to firm debt the ratio takes on very large

values As one way of addressing this problem we trim extremely large values by winsorizing

the ratio at the 90th percentile19 We present results for the subsample where the relative leverage

ratio is defined in Panel A

In Panel A the relative leverage ratio is negatively related to all three risk choices This

expected negative relation is consistent with CEOs talking less risk when they are more

identified with debt holders The relation however is significant only for Book Leverage In

contrast the scaled total sensitivity is positively and significantly related to all three risk choices

in this subsample Because the relative leverage ratio has a negative predicted sign and total

sensitivity has a positive predicted sign we take absolute values to compare the coefficient

magnitudes The average coefficient on scaled sensitivity (0244) is significantly greater than the

absolute value of the average coefficient on the relative leverage ratio (0045) suggesting that

scaled sensitivity explains risk choices better 17 Again because the relative incentive ratio is almost perfectly correlated with the relative leverage ratio results with the relative incentive ratio are virtually identical and therefore we do not tabulate those results 18 An important difference is in the control for delta We include delta scaled by wealth in our regressions as a proxy for risk aversion due to concentration in firm stock and find it to be highly negatively associated with risk-taking as predicted Cassell et al (2012) include delta as part of a composite variable that combines delta vega and the CEOrsquos debt equity ratio and the variable is generally not significant 19 If instead we winsorize the relative leverage ratio at the 99th percentile it is not significant in any specification

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

25

As another way of addressing the problem of extreme values in the relative leverage ratio

Cassell et al (2012) take the natural logarithm of the ratio this solution (which eliminates CEOs

with no inside debt) results in a further reduction in sample size to a maximum of 3329 CEO-

years

We present results for the subsample where ln(Relative Leverage) is defined in Panel B

Unlike the relative leverage ratio the logarithm of the relative leverage ratio has the expected

negative and significant relation with all three risk choices The scaled total sensitivity is also

positively and significantly related to each of the risk choices The average coefficient on scaled

sensitivity (0209) is significantly greater than the absolute value of the average coefficient on

the logarithm of the relative leverage ratio (0155) suggesting that scaled sensitivity explains

risk choices better

Overall the results in Table 6 indicate that the scaled total sensitivity measure better

explains risk-taking choices than the relative leverage ratio and its logarithm In addition the

total sensitivity measure is defined for more CEO-years than the relative leverage ratio or its

natural logarithm and can be used to study incentives in a broader sample of firms

44 Association of vega and equity sensitivity with firm risk choices ndash 1994-2005

On the whole Tables 4 and 5 suggest that the total sensitivity measure better explains

future firm risk choices than either vega or the relative leverage ratio Our inference however is

limited by the fact that we can only compute the total sensitivity measure beginning in 2006

when data on inside debt become available In addition our 2006-2010 sample period contains

the financial crisis a time of unusual shocks to returns and to return volatility which may have

affected both incentives and risk-taking

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

26

In this section we attempt to mitigate these concerns by creating a sample with a longer

time-series from 1994 to 2005 that is more comparable to the samples in Coles et al (2006) and

Hayes et al (2012) To create this larger sample we drop the requirement that data be available

on inside debt Recall from Table 3 that most CEOs have very low incentives from inside debt

and that the equity sensitivity and total sensitivity are highly correlated (099) Consequently we

compute the equity sensitivity as the sum of the stock and option sensitivities (or equivalently as

the total sensitivity minus the debt sensitivity)

Although calculating the equity sensitivity does not require data on inside debt it does

require data on firm options outstanding and this variable was not widely available on

Compustat before 2004 We supplement Compustat data on firm options with data hand-

collected by Core and Guay (2001) Bergman and Jentner (2007) and Blouin Core and Guay

(2010) We are able to calculate the equity sensitivity for 10048 firms from 1994-2005 The

sample is about 61 of the sample size we would obtain if we used the broader sample from

1992-2005 for which we can calculate the CEOrsquos vega

In Table 7 we repeat our analysis in Table 4 for this earlier period using the equity

sensitivity in place of total sensitivity Panel A compares the results using vega and equity

sensitivity for our three risk choices Vega has the expected positive relation with ln(Stock

Volatility) in this earlier sample unlike in our main sample though the relation is insignificant

As in Table 4 vega has a significantly positive association with RampD Expense and a

significantly negative association with Book Leverage20 At the bottom of the panel we find that

the average coefficient on vega (0018) is not significantly greater than zero suggesting that

overall vega is not significantly associated with the three risk choices In contrast the total

20 The book leverage regressions include controls based on Hayes et al (2012) and the results therefore are not directly comparable to the Coles et al (2006) findings

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

27

sensitivity is positive and significant in all three specifications (Columns 4 to 6) The average

coefficient on total sensitivity (0095) is significantly greater than zero Finally the average

coefficient on total sensitivity is significantly greater than the average coefficient on vega

suggesting that total sensitivity better explains risk choices than vega

In Panel B the scaled vega has significantly positive associations with ln(Stock Volatility)

and RampD Expense However scaled vega has an insignificant negative association with Book

Leverage The sum of the three coefficients on scaled vega however is significantly greater than

zero The scaled equity sensitivity is both positively and significantly related to all three risk

variables As in Table 4 Panel B the average coefficient on both scaled vega and scaled equity

sensitivity are significantly greater than zero suggesting that both variables explain risk choices

However the average coefficient on scaled sensitivity (0181) is significantly greater than the

average coefficient on scaled vega (0072) suggesting that scaled sensitivity explains risk

choices better

The results in Table 7 suggest that our inferences from our later sample also hold in the

earlier period 1994-2005

45 Robustness tests

451 Endogeneity

Our previous analysis is based on OLS regressions of risk choices at t+1 and incentives

at t These models are well-specified under the assumption that incentives are predetermined or

exogenous that is incentives at time t are uncorrelated with the regression errors for time t+1

risk choices To assess the sensitivity of our results to this assumption we re-estimate our

models using two-stage least squares

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

28

In the first stage we model the incentive variables (vega delta and total sensitivity) and

the incentive variables scaled by wealth We model each incentive variable as a linear

combination of (1) second-stage control variables that explain risk choices and (2) instruments

that explain incentives but not risk choices We use the following instruments employed by

Armstrong and Vashishtha (2012) and Cassell et al (2013) cash and short-term investments as a

percentage of total assets current year return on assets current and prior year stock returns CEO

age and the personal income tax rate of the state in which the firm has its headquarters In our

models for RampD Expense and Book Leverage we use current year volatility as an additional

instrument (Coles et al 2006) In addition to these instruments we include an indicator for

whether CEOrsquos salary exceeds $1 million CEOs with salaries over $1 million are more likely to

defer compensation to increase the tax deductibility of this compensation to the firm Finally in

our models for the level of vega total sensitivity and delta we include the CEOrsquos total wealth

(This variable is a control variable in our scaled models so it cannot be used as an instrument for

the scaled incentive variables) As discussed above we expect CEOs with higher outside wealth

to have more incentives

Panel A of Table 8 shows first-stage results for a two-stage least squares model for

ln(Stock Volatility) from 2006 to 2010 The number of observations in this specification (5916)

is slightly lower than for the corresponding specification in Table 4 due to missing values of the

instruments In Panel A we show the controls first followed by the instruments The partial F-

statistics at the bottom of the panel indicate that the instruments provide a significant amount of

incremental explanatory power In untabulated analysis we compute Hansenrsquos (1982) J-statistic

for overidentification for each of our models The J-statistic provides a test of model

specification by testing whether the instruments are uncorrelated with the estimated error terms

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

29

None of the J-statistics are significantly different from zero which suggests that the exclusion

restrictions hold for our instruments and that our models are not mispecified

To conserve space we do not present first-stage results for our models for RampD and

leverage The results are very similar in that the instruments add a significant amount of

incremental explanatory power and none of the J-statistics are significantly different from zero

Panel B shows 2SLS coefficients and t-statistics for the second-stage regressions using

the unscaled incentive variables These are analogous to the OLS regression results in Table 4

Panel A In the regression for ln(Stock Volatility) vega is positive (unlike Table 4) but

insignificant As in Table 4 vega has a significant positive association with RampD Expense and a

significant negative association with Book Leverage21 In contrast to Table 4 total sensitivity has

a significant positive association with ln(Stock Volatility) Total sensitivity also has significant

positive associations with RampD Expense and Book Leverage The average 2SLS coefficient on

total sensitivity is significantly larger than that on vega

In Panel C the 2SLS estimates for scaled vega produce different inference than the OLS

estimates in Table 4 Panel B Scaled vega remains positive and significant in Column (2) but

changes sign in Columns (1) and (3) and becomes significantly negative in Column (3) The

average 2SLS coefficient on scaled vega is still significantly positive however Scaled total

sensitivity remains positive in all three regressions but is only marginally significant in the

models for ln(Stock Volatility) (t-statistic = 180) and for Book Leverage (t-statistic = 166) The

average 2SLS coefficient on scaled total sensitivity is significantly larger than that on scaled

vega

21 As in Table 4 the variables are standardized so that for example the 1006 coefficient on vega in Column (2) indicates that a one standard deviation increase in instrumented vega is associated with a 1006 standard deviation increase in RampD Expense

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

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Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

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Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

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Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

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issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

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of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

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Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

30

A concern with 2SLS is that if instruments are weak confidence intervals can be too

small leading to false rejections (Stock and Yogo 2005) To ensure that our inference is robust

we also compute Anderson-Rubin (AR 1949) 95 confidence intervals (untabulated)22 These

intervals give consistent inference when the first stage is weak (Chernozhukov and Hansen

2008) If the confidence interval contains only positive (negative) values the coefficient is

significantly greater (less) than a zero and we indicate this in bold print in Panels B and C In

Panel B this analysis confirms that vega has a significant positive association with RampD

Expense and that total sensitivity has a positive and significant associations with ln(Stock

Volatility) RampD Expense and Book Leverage In Panel C the analysis confirms that vega has a

significant positive association with RampD Expense and total sensitivity has a positive and

significant association with RampD Expense This more conservative procedure does not find a

significant association between vega and Book Leverage scaled vega and Book Leverage and

between scaled total sensitivity and ln(Stock Volatility) and Book Leverage Unfortunately we

could not compute Anderson-Rubin confidence intervals for the average coefficients or their

differences

In untabulated results we find that the 2SLS results for the 1994-2005 sample produce

similar inference to that in Table 6 Equity sensitivity explains risk choices better than vega

Overall our results using two-stage least squares to address endogeneity are consistent with our

earlier conclusions from Table 4 total sensitivity explains risk choices better than vega We note

that while the 2SLS results mitigate concerns about endogeneity we cannot completely eliminate

endogeneity as a potential confounding factor

452 Changes in vega changes in equity sensitivity and changes in firm risk choices

22 We compute the intervals using Stata code ldquoweakivrdquo developed by Finlay Magnusson and Schaffer (2013)

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

31

A second way of addressing the concern about incentives being endogenous is to identify

an exogenous change that affects incentives but not risk-taking Hayes et al (2012) use a change

in accounting standards which required firms to recognize compensation expense for employee

stock options beginning in December 2005 Firms responded to this accounting expense by

granting fewer options Hayes et al (2012) argue that if the convex payoffs of stock options

cause risk-taking this reduction in convexity should lead to a decrease in risk-taking

We follow Hayes et al (2012) and estimate Eqs (12) and (13) using changes in the mean

value of the variables from 2002 to 2004 and from 2005 to 2008 (For dependent variables we

use changes in the mean value of the variables from 2003 to 2005 and 2006 to 2009) We use all

available firm-years to calculate the mean and require at least one observation per firm in both

the 2002-2004 and 2005-2008 periods

Table 9 shows the results of these regressions Similar to Hayes et al (2012) we find that

the change in vega is negatively but not significantly related to the change in our three risk

choices (Panel A) The change in equity sensitivity is also negative and insignificant using the

change in stock volatility is positive but insignificant using RampD and positive and significant

using leverage The average coefficient on the change in vega (-0020) is insignificantly negative

The average coefficient on the change in equity sensitivity (0041) is significantly positive The

difference between the average coefficients is significant

When we examine instead the scaled measures in Panel B the change in scaled vega is

again is not significantly related to any of the risk choices In contrast the change in scaled

equity sensitivity is significantly positively related to the change in stock volatility in Column (4)

and leverage in Column (6) The average coefficient on the change in scaled vega is positive

(0014) but insignificant The average coefficient on the change in scaled equity sensitivity

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

32

(0105) is an order of magnitude larger and highly significant The difference between the

average coefficients is again significant Scaled equity sensitivity explains the change in risk

choices around the introduction of option expensing under SFAS 123R better than scaled vega

does

453 Convexity in long-term incentive awards

Another concern with our analysis is that firms may have responded to stock option

expensing by replacing the convexity in options with the convexity in long-term incentive

awards (Hayes et al 2012) These plans are more heavily used since the change in stock option

expensing in 2005 so this concern is greatest in our 2006-2010 sample period As discussed in

Hayes et al typical long-term incentive awards (LTIAs) deliver a number of shares to the CEO

that varies from a threshold number to a target number to a maximum number as a function of

firm performance When the number of shares vested in these plans is explicitly or implicitly

based on stock price performance variation in the number of shares vested as a function of the

share price can create incentives to increase volatility (Bettis et al 2013)

To estimate the risk-taking incentives provided by LTIAs we follow the procedure

described in Hayes et al (2012 p 186) and in the related internet appendix (Hayes et al 2011)

The procedure assumes that the grant vests in three years and that the degree of vesting is a

function of stock price performance during those three years23 This procedure allows us to

estimate the value vega and delta for each grant

We find that 36 of our sample CEO received LTIA grants from 2006-2010 Following

the Hayes et al procedure we compute the convexity of these LTIA grants We find the mean

23 Most LTIAs make vesting contingent on accounting numbers such as earnings and sales To value the grants procedures in Hayes et al (2012) and Bettis et al (2013) assume a mapping from accounting numbers into stock returns

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

33

convexity to be $392 thousand which is consistent with though slightly larger than the mean of

$156 thousand computed by Hayes et al for the 2002-2008 period

The portfolio values are of direct interest for our study Under the assumption that the

grants vest in three years the portfolio of LTIA incentives is the sum of the incentives from this

yearrsquos grant and from the grants in the two previous two years For example for a CEO in 2006

we compute LTIA convexity as the sum of grants from 2004 2005 and 2006 We re-compute

the incentives of earlier yearsrsquo grants to reflect their shorter time to maturity and changes in

prices and volatility For the 45 of CEOs who have current or past LTIA grants we compute

portfolio convexity of $577 thousand24 When averaged with CEOs without LTIAs the average

portfolio LTIA convexity computed as the change in LTIA value for a 1 change in volatility

is $252 thousand approximately 6 of the sample mean vega shown in Table 4 (We are unable

to calculate the LTIA value for 18 CEO-years in our sample) Similarly we compute portfolio

LTIA sensitivity which incorporates increases in equity value due to reductions in debt value to

be $335 thousand or approximately 5 of the sample mean sensitivity shown in Table 425

In Table 10 we show regression results for our main sample in which the incentive

variables include LTIA convexity Adding the LTIA incentives does not affect our inference

However we caveat that our estimates are noisy because data on LTIA plans is not well-

disclosed26

24 Note that the portfolio which may contain as many as three grants has average convexity of $577 thousand which is only about 47 greater than grant convexity of $392 thousand This occurs because (1) some CEOs do not receive grants each year and (2) as with a standard option the convexity of an LTIA grant falls as it goes farther in the money 25 Similar to our main sample computations above we compute LTIA sensitivity to incorporate increases in equity value due to reductions in debt value Because the total number of shares awarded to all employees under LTIA plans is not disclosed however we do not adjust for the potential dilution from these plans 26 Like Hayes et al (2011 2012) we base our estimates on LTIA data from Execucomp More detailed data on LTIAs is available from IncentiveLab but this data set covers only about 60 of the Execucomp sample and concentrates on larger firms

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

34

454 Other robustness tests

We examine incentives from CEOsrsquo holdings of debt stock and options CEOsrsquo future

pay can also provide risk incentives but the direction and magnitude of these incentives are less

clear On the one hand future CEO pay is strongly related to current stock returns (Boschen and

Smith 1995) and CEO career concerns lead to identification with shareholders On the other

hand future pay and in particular cash pay arguably is like inside debt in that it is only valuable

to the CEO when the firm is solvent Therefore the expected present value of future cash pay can

provide risk-reducing incentives (eg John and John 1993 Cassell et al 2012) By this

argument total risk-reducing incentives should include future cash pay as well as pensions and

deferred compensation27 To evaluate the sensitivity of our results we estimate the present value

of the CEOrsquos debt claim from future cash pay as current cash pay multiplied by the expected

number of years before the CEO terminates Our calculations follow those detailed in Cassell et

al (2012) We add this estimate of the CEOrsquos debt claim from future cash pay to inside debt and

recalculate the relative leverage ratio and the debt sensitivity Adding future cash pay

approximately doubles the risk-reducing incentives of the average manager Because risk-

reducing incentives are small in comparison to risk-increasing incentives our inferences remain

unchanged

Second our estimate of the total sensitivity to firm volatility depends on our estimate of

the debt sensitivity As Wei and Yermack discuss (2011 p 3826-3827) estimating the debt

sensitivity can be difficult in a sample where most firms are not financially distressed To

address this concern we attempt to reduce measurement error in the estimates by using the mean

estimate for a group of similar firms To do this we note that leverage and stock volatility are the

27 Edmans and Liu (2011) argue that the treatment of cash pay in bankruptcy is different than inside debt and therefore provides less risk-reducing incentives

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

35

primary observable determinants of the debt sensitivity We therefore sort firms each year into

ten groups based on leverage and then sort each leverage group into ten groups based on stock

volatility For each leverage-volatility-year group we calculate the mean sensitivity as a

percentage of the book value of debt We then calculate the debt sensitivity for each firm-year as

the product of the mean percentage sensitivity of the leverage-volatility-year group multiplied by

the total book value of debt We use this estimate to generate the sensitivities of the CEOrsquos debt

stock and options We then re-estimate our results in Tables 4 6 and 7 Our inference is the

same after attempting to mitigate measurement error in this way

Finally our sensitivity estimates do not include options embedded in convertible

securities While we can identify the amount of convertibles the number of shares issuable upon

conversion is typically not available on Compustat Because the parameters necessary to estimate

the sensitivities are not available we repeat our tests excluding firms with convertible securities

To do this we exclude firms that report convertible debt or preferred stock In our main

(secondary) sample 21 (26) of all firms have convertibles When we exclude these firms

our inferences from Tables 4 6 and 7 are unchanged

5 Conclusion

We measure the total sensitivity of managersrsquo debt stock and option holdings to changes

in firm volatility Our measure incorporates the option value of equity the incentives from debt

and stock and values options as warrants We examine the relation between our measure of

incentives and firm risk choices and compare the results using our measure and those obtained

with vega and the relative leverage ratio used in the prior literature Our measure explains risk

choices better than the measures used in the prior literature We also calculate an equity

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

36

sensitivity that ignores debt incentives and find that it is 99 correlated with the total sensitivity

While we can only calculate the total sensitivity beginning in 2006 when we examine the equity

sensitivity over an earlier 1994-2005 period we find consistent results Our measure should be

useful for future research on managersrsquo risk choices

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

37

Appendix A Measurement of firm and manager sensitivities (names in italics are Compustat variable names) A1 Value and sensitivities of employee options We value employee options using the Black-Scholes model modified for warrant pricing by Galai and Schneller (1978) To value options as warrants W the firmrsquos options are priced as a call on an identical firm with no options

lowast lowast lowastlowast (A1)

We simultaneously solve for the price lowast and volatility lowast of the identical firm using (A2) and (A3) following Schulz and Trautmann (1994)

lowast lowast lowast lowastlowast (A2)

1 lowastlowast

lowast (A3)

Where

P = stock price lowast = share price of identical firm with no options outstanding = stock-return volatility (calculated as monthly volatility for 60 months with a minimum of

12 months) lowast = return volatility of identical firm with no options outstanding

q = options outstanding shares outstanding (optosey csho) δ = natural logarithm of the dividend yield ln(1+dvpsx_f prcc_f)

= time to maturity of the option N = cumulative probability function for the normal distribution lowast ln lowast lowast lowast

X = exercise price of the option r = natural logarithm one plus the yield of the risk-free interest rate for a four-year maturity

The Galai and Schneller (1978) adjustment is an approximation that ignores situations when the option is just in-the-money and the firm is close to default (Crouhy and Galai 1994) Since leverage ratios for our sample are low (see Table 2) bankruptcy probabilities are also low and the approximation should be reasonable A2 Value of firm equity We assume the firmrsquos total equity value E (stock and stock options) is priced as a call on the firmrsquos assets

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

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Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

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Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

38

lowast ´ ´ (A4) Where

lowast lowast ´ (A5)

V = firm value lowast = share price of identical firm with no options outstanding (calculated above)

n = shares outstanding (csho)

lowast = return volatility of identical firm with no options outstanding (calculated above)

= time to debt maturity lowast lowast

following Eberhart (2005)

N = cumulative density function for the normal distribution ´ ln

F = the future value of the firmrsquos debt including interest ie (dlc + dltt) adjusted following Campbell et al (2008) for firms with no long-term debt

= the natural logarithm of the interest rate on the firmrsquos debt ie ln 1 We

winsorize the interest to have a minimum equal to the risk-free rate r and a maximum equal to 15

A3 Values of firm stock options and debt We then estimate the value of the firmrsquos assets by simultaneously solving (A4) and (A5) for V and We calculate the Black-Scholes-Merton value of debt as

1 ´ ´ (A6) The market value of stock is the stock price P (prcc_f) times shares outstanding (csho) To value total options outstanding we multiply options outstanding (optosey) by the warrant value W estimated using (A1) above Because we do not have data on individual option tranches we assume that the options are a single grant with weighted-average exercise price (optprcey) We follow prior literature (Cassell et al 2012 Wei and Yermack 2011) and assume that the time to maturity of these options is four years A4 Sensitivities of firm stock options and debt to a 1 increase in volatility We increase stock volatility by 1 101 This also implies a 1 increase in firm volatility We then calculate a new Black-Scholes-Merton value of debt ( ´) from (A6) using V and the new firm volatility The sensitivity of debt is then ´

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

39

The new equity value is the old equity value plus the change in debt value ( lowast´ lowast ´) Substituting this equity value and into (A2) and (A3) we calculate a new P and lowast The stock sensitivity is ´ The option sensitivity is difference between the option prices calculated in (A1) using the two sets of equity and lowast values ´ A51 Sensitivities of CEO stock options debt and stock The CEOrsquos stock sensitivity is the CEOrsquos percentage ownership of stock multiplied by the firmrsquos stock sensitivity shown in Appendix A4 above

´ (A7) Where

is the CEOrsquos ownership of stock shares (shrown_excl_opts) divided by firm shares outstanding (csho)

Similarly the CEOrsquos debt sensitivity is

´ (A8) Where

follows Cassell et al (2012) and is the CEOrsquos ownership inside debt (pension_value_tot plus defer_balance_tot) divided by firm debt (dlc plus dltt)

Following Core and Guay (2002) we value the CEOrsquos option portfolio as one grant of exercisable options with an assumed maturity of 6 years and as one grant of unexercisable options with an assumed maturity of 9 years The CEOrsquos option sensitivity is the difference between the values of the CEOrsquos option portfolio calculated using these parameters and the equity and lowast values from above

´ (A9) A52 Vega and delta We follow the prior literature and compute vega and delta using the Black-Scholes-Merton formula to value options

(A10) Where

is the number of options in the CEOrsquos portfolio X and follow the Core and Guay (2002) assumptions about option tranches and

option maturities (in general that unexercisable options have a maturity of 9 years and that exercisable options have a maturity of 6 years)

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

40

To make our calculation of vega comparable to the total sensitivity we calculate vega as the difference between the standard Black-Scholes-Merton value in (A10) at and

´ (A11) Using the derivative of the Black-Scholes-Merton equation (A10) the sensitivity of an option to a change in the price is

(A12)

The sensitivity of the CEOrsquos stock and option portfolio to a 1 increase in stock price (the ldquodeltardquo) is

lowast 001 lowast lowast lowast 001 lowast (A13) A53 Relative sensitivity ratio If the sensitivity of stock price to volatility is positive the ratio is

(A14a)

If the sensitivity of stock price to volatility is negative the ratio is

(A14b)

A54 Relative leverage ratio Following Sundaram and Yermack (2007) the relative leverage ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage equity holdings

(A15)

Where

= sum of the value of the CEOrsquos stock holding and the Black-Scholes value of the CEOrsquos option portfolio calculated from (A10) following Core and Guay (2002)

= sum of the market value of stock and the Black-Scholes value of options calculated according to (A10) above using the firm parameters from Appendix A3

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

41

A55 Relative incentive ratio

Following Wei and Yermack (2011) the relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta

(A16)

Where = sum of the delta of the CEOrsquos stock holding and the Black-Scholes delta of the

CEOrsquos option portfolio as in (A13) calculated following Core and Guay (2002) = sum of the number of shares outstanding and the delta of the options calculated

according to (A13) above using the firm parameters from Appendix A3

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

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taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

42

Appendix B Measurement of Other Variables The measurement of other variables with the exception of Total Wealth and State Income Tax Rate is based on compensation data in Execucomp financial statement data in Compustat and stock market data from the Center for Research in Security Prices (CRSP) database Dependent Variables

ln(Stock Volatility) The natural logarithm of the variance of daily stock returns over fiscal year t+1

RampD Expense The ratio of the maximum of zero and RampD expense (xrd) to total assets (at) for fiscal year t+1

Book Leverage The ratio of long-term debt (dlc + dltt) to total assets (at) at fiscal year t+1

ln(Asset Volatility) The natural logarithm of the variance of firm value calculated using Eq (A5) in fiscal year t+1

ln(Systematic Volatility) The natural logarithm of the variance of systematic daily stock returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

ln(Idiosyncratic Volatility) The natural logarithm of the variance of residual daily returns over fiscal year t+1 Systematic returns estimated using the Fama and French (1993) three factor model over the previous 36 months

Control Variables

CEO Tenure The tenure of the CEO through year t Cash Compensation The sum of salary (salary) and bonus compensation (bonus) ln(Sales) The natural logarithm of total revenue (revt) Market-to-Book The ratio of total assets (at) minus common equity (ceq) plus the

market value of equity (prcc_f csho) to total assets CAPEX The ratio of capital expenditures (capx) less sales of property

plant and equipment (sppe) to total assets (at) Surplus Cash The ratio of net cash flow from operations (oancf) less

depreciation (dpc) plus RampD expense (xrd) to total assets (at) If depreciation expense is missing (dpc) and if PPE is less than 1 of total assets we set depreciation expense to zero

ln(Sales Growth) The natural logarithm of the quantity total revenue in year t (revtt) divided by sales in year t-1 (revtt-1)

Return The stock return over the fiscal year ROA The ratio of operating income before depreciation (oibdp) to total

assets (at) PPE The ratio of net property plant and equipment (ppent) to total

assets (at) Modified Z-Score The quartile rank by year of the modified Altman (1968) Z-Score

33 oiadp at + 12 (act ndash lct) at + sale at + 14 re at Rating An indicator variable set to one when the firm has a long-term

issuer credit rating from SampP

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

43

Total Wealth The sum of non-firm wealth calculated according to Dittman and Maug (2007) (non_firm_wealth available from httppeoplefeweurnldittmanndatahtm and set to missing when negative) stock holdings (shrown_excl_opts prcc_f) and CEO options valued as warrants following Eq (A9) in A51 above and inside debt (pension_value_tot plus defer_balance_tot) beginning in 2006

Instruments

Cash Ratio The ratio of cash and short-term investments (che) to total assets (at)

State Income Tax Rate The maximum state tax rate on individual income calculated using the TAXSIM model (Feenberg and Coutts 1993) and obtained from httpwwwnberorg~taxsimstate-rates Set to zero for firms outside the United States

CEO Age The age of the CEO in year t High Salary An indicator variable set to one when salary is greater than $1

million ln(Monthly Stock

Volatility) The natural logarithm of the variance of monthly stock returns

over the previous 60 months requiring at least 12 observations

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

44

References Altman E 1968 Financial ratios discriminant analysis and the prediction of corporate bankruptcy Journal of

Finance 23 589-609 Anderson TW Rubin H 1949 Estimation of the Parameters of a Single Equation in a Complete System of

Stochastic Equations Annals of Mathematical Statistics 20 46-63 Armstrong CS Larcker DF Ormazabal G Taylor DJ 2013 The relation between equity incentives and

misreporting The role of risk-taking incentives Journal of Financial Economics 109 327-350 Armstrong C Vashishtha R 2012 Executive stock options differential risk-taking incentives and firm value

Journal of Financial Economics 104 70-88 Bergman N Jentner D 2007 Employee sentiment and stock option compensation Journal of Financial

Economics 84 667-712 Bettis C Bizjak J Coles J Kalpathy S 2013 Performance-vesting provisions in executive compensation

Working paper Arizona State University Available at SSRN httpssrncomabstract=2289566 Bharath ST Shumway T 2008 Forecasting default with the Merton distance to default model Review of

Financial Studies 21 1339-1369 Black F Scholes M 1973 The pricing of options and corporate liabilities Journal of Political Economy 81 637-

654 Blouin J Core J Guay W 2010 Have the tax benefits of debt been overestimated Journal of Financial

Economics 98 195-213 Boschen JF Smith KJ 1995 You Can Pay Me Now and You Can Pay Me Later The Dynamic Response of

Executive Compensation to Firm Performance Journal of Business 68 577-608 Campbell J Hilscher J Szilagyi J 2008 In search of distress risk Journal of Finance 63 2899-2939 Cassell C Huang S Sanchez J Stuart M 2012 Seeking safety The relation between CEO inside debt holdings

and the riskiness of firm investment and financial policies Journal of Financial Economics 103 588-610 Chernozhukov V Hansen C 2008 The reduced form A simple approach to inference with weak instruments

Economic Letters 100 68-71 Coles J Daniel N Naveen L 2006 Managerial incentives and risk-taking Journal of Financial Economics 79

431-468 Conyon M Core J Guay W 2011 Are US CEOs paid more than UK CEOs Inferences from risk-adjusted

pay Review of Financial Studies 24 402-438 Core J Guay W 2001 Stock option plans for non-executive employees Journal of Financial Economics 61 253-

287 Core J Guay W 2002 Estimate the value of employee stock option portfolios and their sensitivities to price and

volatility Journal of Accounting Research 40 613-630 Crouhy M Galai D 1994 The interaction between the financial and investment decisions of the firm The case of

issuing warrants in a levered firm Journal of Banking and Finance 18 861-880

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

45

Dittmann I Maug E 2007 Lower Salaries and No Options On the Optimal Structure of Executive Pay Journal

of Finance 62 303-343 Eberhart A 2005 A comparison of Mertonrsquos option pricing model of corporate debt valuation to the use of book

values Journal of Corporate Finance 11 401-426 Edmans A Liu Q 2011 Inside debt Review of finance 15 75-102 Fama EF French KR 1993 Common risk factors in the returns on stocks and bonds Journal of Financial

Economics 33 3-56 Feenberg D Coutts E 1993 An introduction to the TAXSIM model Journal of Policy Analysis and Management

12 189-194 Finlay K Magnusson LM Schaffer ME 2013 weakiv Weak-instrument-robust tests and confidence intervals

for instrumental-variable (IV) estimation of linear probit and tobit models httpideasrepecorgcbocbocodes457684html

Galai D Schneller M 1978 Pricing of warrants and the value of the firm Journal of Finance 33 1333-1342 Guay W 1999 The sensitivity of CEO wealth to equity risk An analysis of the magnitude and determinants

Journal of Financial Economics 53 43-71 Hayes RM Lemmon M Qui M 2011 Internet appendix for ldquoStock options and managerial incentives for risk-

taking Evidence from FAS 123Rrdquo httpjferochestereduHayes_Lemmon_Qiupdf Hayes R Lemmon M Qiu M 2012 Stock options and managerial incentives for risk taking Evidence from

FAS 123R Journal of Financial Economics 105 174-190 Hall BJ Murphy KJ 2002 Stock options for undiversified executives Journal of Accounting and Economics 33

3-42 Hansen LP 1982 Large sample properties of generalized method of moments estimators Econometrica 50 1029-

1054 Hillegeist SA Keating EK Cram DP Lundstedt KG 2004 Assessing the probability of bankruptcy Review

of Accounting Studies 9 5-34 Jensen M Meckling W 1976 Theory of the firm Managerial behavior agency costs and ownership structure

Journal of Financial Economics 3 305-360 John T John K 1993 Top-management compensation and capital structure Journal of Finance 48 949-974 Lewellen K 2006 Financing decisions when managers are risk averse Journal of Financial Economics 82 551-

589 Merton R 1973 Theory of rational option pricing Bell Journal of Economics and Management Science 4 141-183 Merton R 1974 On the pricing of corporate debt The risk structure of interest rates Journal of Finance 29 449-

470 Schulz G Trautmann S 1994 Robustness of option-like warrant valuation Journal of Banking and Finance 18

841-859

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

46

Stock JH Yogo M 2005 Testing for weak instruments in linear IV regression In Andrews DWK Stock JH (Eds) Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg Cambridge University Press New York pp 80-108

Sundaram R Yermack D 2007 Pay me later Inside debt and its role in managerial compensation Journal of

Finance 62 1551-1588 Wei C Yermack D 2011 Investor reactions to CEOsrsquo inside debt incentives Review of Financial Studies 24

3813-3840

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

47

Table 1 Panel A Example firm -- Sensitivity of debt stock and options to firm volatility ($ Thousands) The example firm has a $25 billion market value of assets and a firm volatility of 35 Options are 7 of shares outstanding and have a price-to-strike ratio of 14 The options and the debt have a maturity of four years Leverage is the face value of debt divided by the market value of assets All values and sensitivities are calculated using Black-Scholes formulas assuming an interest rate of 225 and no dividends Options are valued as warrants following Schulz and Trautmann (1994) The debt stock and option sensitivity is the dollar change in value for a 1 increase in firm volatility The equity sensitivity is the total stock and option sensitivity

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity (1) (2) (3) (4) (5)

001 $ 0 ($ 287) $ 287 $ 0

4 $ 0 ($ 290) $ 290 $ 0

14 ($ 49) ($ 247) $ 296 $ 49

25 ($ 471) $ 154 $ 317 $ 471

50 ($2856) $ 2441 $ 415 $ 2856

Leverage Debt Sens Debt Value

Stock Sens Stock Value

Option Sens Option Value

Equity Sens Equity Value

(1) (2) (3) (4) (5)

001 000 -001 040 000

4 000 -001 042 000

14 -001 -001 045 000

25 -008 001 052 003

50 -025 019 084 021

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

48

Panel B CEO The example CEO owns 2 of the firmrsquos debt 2 of the firmrsquos stock and 16 of the firmrsquos options The CEOrsquos debt and stock sensitivity is the CEOrsquos percentage holding times the firm sensitivity from Panel A Vega is the sensitivity of the CEOrsquos option portfolio to a 1 increase in stock volatility The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables

Leverage Debt

Sensitivity Stock

Sensitivity Option

Sensitivity Equity

Sensitivity Total

Sensitivity Vega

Relative Sensitivity

Ratio

Relative Leverage

Ratio

Relative Incentive

Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

001 $ 0 ($ 6) $ 46 $ 40 $ 40 $ 49 013 083 072 4 $ 0 ($ 6) $ 46 $ 41 $ 41 $ 49 013 083 073

14 ($ 1) ($ 5) $ 47 $ 42 $ 41 $ 50 013 082 073 25 ($ 9) $ 3 $ 51 $ 54 $ 44 $ 50 018 082 073 50 ($57) $ 49 $ 66 $ 115 $ 58 $ 44 050 080 072

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

49

Table 2 Sample descriptive statistics This table provides descriptive statistics on the primary sample of 5967 firm-year observations from 2006 to 2010 representing 1574 unique firms Dollar amounts are in millions of dollars We estimate the volatility of asset returns following Eberhart (2005) The market value of debt is calculated as the Black-Scholes-Merton option value of the debt Employee options are valued as warrants following Schulz and Trautmann (1994) using the end-of-year number of stock options outstanding and weighted average strike price and an assumed maturity of 4 years The market value of assets is the sum of market value of stock the market value of debt and the warrant value of employee options All variables are winsorized by year at the 1 tails

Variable Mean Std Dev P1 Q1 Median Q3 P99Volatility of Stock Returns 0482 0235 0163 0318 0426 0583 1330Volatility of Asset Returns 0395 0199 0116 0252 0355 0485 1077Market Value of Stock $ 6944 $ 18108 $ 50 $ 568 $ 1488 $ 4599 $ 117613 Market Value of Debt $ 1501 $ 3491 $ 0 $ 18 $ 259 $ 1155 $ 20703 Market Value of Employee Options $ 119 $ 287 $ 0 $ 9 $ 30 $ 95 $ 1682 Market Value of Assets $ 8879 $ 22102 $ 72 $ 738 $ 2000 $ 6378 $ 145591 Leverage (Book Value of DebtMarket Value of Assets) 0179 0186 0000 0017 0133 0273 0807

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

50

Table 3 Descriptive statistics for incentive variables ($ Thousands) The debt stock and option sensitivity is the dollar change in value of the CEOsrsquo holdings for a 1 increase in firm volatility The equity sensitivity is the sum of the stock and option sensitivities The total sensitivity is the sum of the debt stock and option sensitivities Vega is the sensitivity of the CEOsrsquo option portfolios to a 1 increase in stock volatility Total wealth is the sum of the CEOsrsquo debt stock and option holdings and outside wealth from Dittmann and Maug (2007) The relative sensitivity ratio is the ratio the managerrsquos risk-reducing incentives to his risk-taking incentives The relative leverage ratio is the CEOrsquos percentage debt holdings divided by divided by the CEOrsquos percentage holdings of equity value The relative incentive ratio is the ratio of the CEOrsquos percentage debt holdings divided by the CEOrsquos percentage holdings of delta See Appendix A for detailed definitions of the incentive variables All variables are winsorized by year at the 1 tails All dollar values are in thousands of dollars Panel A Full sample This panel presents descriptive statistics on the sensitivity and incentive measures for the full sample

Variable Mean Std Dev P1 Q1 Median Q3 P99Debt Sensitivity ($ 520) $ 1550 ($ 9378) ($ 200) ($ 000) $ 000 $ 000 Stock Sensitivity $ 1045 $ 4657 ($ 4070) ($ 049) $ 000 $ 455 $ 29060 Option Sensitivity $ 5777 $ 8302 $ 000 $ 875 $ 2742 $ 6874 $ 39907 Equity Sensitivity $ 7198 $ 12542 ($ 1199) $ 1065 $ 3184 $ 8059 $ 75817 Total Sensitivity $ 6540 $ 11562 ($ 3296) $ 878 $ 2819 $ 7457 $ 67563 Vega $ 4915 $ 7101 $ 000 $ 730 $ 2292 $ 5939 $ 34445 Total Wealth $ 102027 $ 256672 $ 1294 $ 13967 $ 32806 $ 80671 $ 1729458 Equity Sensitivity Total Wealth 015 015 000 004 012 022 064Total Sensitivity Total Wealth 014 014 -003 003 010 021 063Vega Total Wealth 011 010 000 003 008 017 043Relative Sensitivity Ratio 042 100 000 001 003 019 444Relative Leverage Ratio 309 1573 000 000 018 118 6799Relative Incentive Ratio 231 1119 000 000 015 091 4844

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

51

Panel B Correlation between Incentive Variables This table shows Pearson correlation coefficients for the incentive measures See Appendix A for detailed definitions of the incentive variables Coefficients greater than 003 in magnitude are significant at the 005 level

Total

Sens Vega Equity

Sens Tot

Wealth Tot Sens Tot Wealth

Vega Tot Wealth

Eq Sens Tot Wealth

Rel Lev

Rel Incent

Rel Sens

Total Sensitivity to Firm Volatility 100 Vega 069 100 Equity Sensitivity to Firm Volatility 099 068 100 Total Wealth 038 028 038 100 Total Sensitivity Total Wealth 024 015 022 -021 100 Vega Total Wealth 010 024 009 -024 079 100 Equity Sensitivity Total Wealth 023 015 023 -023 098 077 100 Relative Leverage Ratio -004 000 -004 -002 -010 -004 -010 100 Relative Incentive Ratio -005 -001 -005 -002 -011 -005 -011 099 100 Relative Sensitivity Ratio -016 -023 -013 014 -032 -037 -029 001 003 100

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

52

Table 4 Comparison of the association between vega and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) CEO Tenure -0029 -0057 0020 -0036 -0054 -0002

(-227) (-393) (108) (-278) (-382) (-014) Cash Compensation -0016 0035 0007 -0029 0045 -0022

(-124) (163) (035) (-269) (207) (-108) ln(Sales) -0339 -0354 -0002 -0371 -0313 -0067

(-1000) (-813) (-008) (-1187) (-764) (-258) Market-to-Book -0130 0028 0112 -0134 0041 0104

(-270) (084) (119) (-265) (125) (112) Book Leverage 0112 0038 0111 0017

(582) (130) (477) (057) RampD Expense 0056 -0084 0042 -0106

(286) (-281) (206) (-349) CAPEX 0034 0035

(155) (156) Surplus Cash 0266 0276

(820) (867) ln(Sales Growth) 0007 0004

(027) (013) Return 0000 -0006

(000) (-013) ROA 0047 0046

(048) (046) PPE 0055 0059

(152) (163) Mod Z-Score -0297 -0270

(-1081) (-1006) Rating 0305 0298

(1209) (1242) Delta 0004 0020 -0058 -0007 0017 -0093

(023) (145) (-253) (-036) (137) (-285) Vega -0061 0151 -0067

(-204) (595) (-351) Total Sensitivity 0014 0097 0121

(060) (463) (496) Observations 5967 5585 5538 5967 5585 5538 Adj R-squared 0464 0404 0274 0462 0396 0281 Avg coefficient 0008 0077 t-statistic 082 838 Diff in avg coef 0069 t-statistic 840

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

53

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

CEO Tenure -0047 0012 0029 -0032 -0015 0057 (-237) (088) (157) (-161) (-097) (361)

Cash Compensation -0029 0054 -0005 -0027 0063 0004 (-265) (272) (-028) (-268) (296) (022)

ln(Sales) -0359 -0274 -0039 -0347 -0272 -0024 (-1246) (-718) (-149) (-1176) (-703) (-104)

Market-to-Book -0096 0082 0121 -0064 0075 0173 (-203) (259) (125) (-144) (227) (189)

Book Leverage 0108 0022 0049 -0031 (571) (078) (193) (-095)

RampD Expense 0038 -0116 0024 -0125 (154) (-346) (100) (-395)

CAPEX 0041 0043 (194) (205)

Surplus Cash 0262 0278 (924) (923)

ln(Sales Growth) 0019 0009 (070) (031)

Return 0022 0005 (069) (015)

ROA 0051 0061 (052) (068)

PPE 0065 0046 (173) (133)

Modified Z-Score -0284 -0226 (-1020) (-880)

Rating 0306 0264 (1261) (1272)

Delta Total Wealth -0184 -0118 -0062 -0234 -0063 -0173 (-807) (-495) (-236) (-1202) (-299) (-499)

Total Wealth 0024 0078 -0041 0039 0061 0003 (123) (416) (-219) (185) (376) (017)

Vega Total Wealth 0049 0254 0092 (159) (752) (252)

Tot Sensitivity Tot Wealth 0165 0177 0351 (492) (470) (715)

Observations 5967 5585 5538 5967 5585 5538 Adjusted R-squared 0484 0424 0275 0497 0406 0343 Average coefficient 0131 0231 t-statistic 595 755 Difference in avg coef 0010 t-statistic 737

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

54

Table 5 Comparison of the association between vega and total sensitivity and alternative volatility measures This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega 0078 -0066 -0065

(242) (-181) (-248) Total Sensitivity 0093 0002 0013

(357) (006) (067)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0534 0536 0448 0446 0498 0495

Difference in coefficients 0015 0068 0078 t-statistic 102 314 649

Panel B Scaled Incentive Variables ln(Asset Volatility) ln(Systematic Volatility) ln(Idiosyncratic Volatility) (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0138 0021 0048 (296) (068) (145)

Total Sens Tot Wealth 0157 0119 0173 (301) (366) (483)

Observations 5967 5967 5967 5967 5967 5967 Adjusted R-squared 0546 0549 0453 0460 0516 0531

Difference in coefficients 0018 0098 0124 t-statistic 079 563 1008

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

55

Table 6 Comparison of the association between relative leverage and total sensitivity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) Relative Leverage Ratio -0010 -0011 -0114

(-123) (-123) (-305) Tot Sens Tot Wealth 0200 0170 0360

(502) (433) (685)

Observations 4994 4703 4647 4994 4703 4647 Adjusted R-squared 0496 0363 0245 0517 0383 0315 Average coefficient -0045 0244 t-statistic 344 717 Diff in absolute value of avg coef 0199 t-statistic 556

Panel B Log of Relative Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6) ln(Rel Lev Ratio) -0141 -0033 -0290

(-508) (-222) (-929) Tot Sens Tot Wealth 0220 0091 0318

(538) (352) (903)

Observations 3329 3180 3120 3329 3180 3120 Adjusted R-squared 0532 0403 0408 0543 0413 0400 Average coefficient -0155 0209 t-statistic 953 850 Diff in absolute value of avg coef 0055 t-statistic 185

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

56

Table 7 Comparison of the association between vega and equity sensitivity and future volatility RampD and leverage from 1994-2005 This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0035 0089 -0070

(127) (485) (-370) Equity Sensitivity 0058 0072 0156

(269) (605) (517)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0550 0343 0317 0552 0342 0330

Average coefficient 0018 0095 t-statistic 144 663

Difference in avg coef 0077 t-statistic 539

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Tot Wealth 0103 0131 -0017 (551) (613) (-074)

Equity Sens Tot Wealth 0196 0058 0288 (1347) (325) (1104)

Observations 10048 9548 9351 10048 9548 9351 Adjusted R-squared 0579 0347 0315 0594 0340 0363

Average coefficient 0072 0181 t-statistic 584 1421

Difference in avg coef 0108 t-statistic 1056

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

57

Table 8 Comparison of two-stage least squares estimates of the relation between vega and total sensitivity and future volatility RampD and leverage for 2006 to 2010

This table presents two-stage least squares estimates First-stage results for the model for ln(Stock Volatility) are shown in Panel A Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Other variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A First-stage estimates of incentive variables

Vega Delta Tot Sens Vega

Tot Wealth Delta

Tot Wealth Tot Sens Tot Wealth

(1) (2) (3) (4) (5) (6) Control Variables CEO Tenure 0098 0005 0095 -0248 -0050 -0172

(366) (030) (488) (-1485) (-236) (-1055) Cash Compensation 0135 0013 0151 0010 0003 -0005

(344) (124) (284) (071) (020) (-044) ln(Sales) 0422 0046 0208 0048 0099 0002

(855) (249) (560) (161) (357) (009) Market-to-Book 0099 0057 -0018 -0111 0134 -0145

(459) (447) (-081) (-400) (355) (-631) Book Leverage -0020 -0007 0193 0053 -0020 0374

(-120) (-072) (741) (259) (-102) (1115) RampD Expense 0164 0006 0096 0238 0079 0141

(559) (059) (485) (728) (307) (428) CAPEX -0013 0023 0028 -0008 0010 0002

(-053) (218) (135) (-040) (041) (011) Total Wealth -0141 0062 -0121

(-587) (201) (-586) Instruments Cash Ratio 0040 -0010 0045 0070 -0036 0053 (191) (-106) (250) (319) (-158) (298) Returnt -0028 0017 0023 -0063 0104 -0025 (-110) (186) (132) (-188) (164) (-068) Returnt-1 -0023 0006 0024 -0066 0030 -0034 (-144) (157) (134) (-284) (122) (-115) ROA -0030 -0016 -0048 -0018 0039 -0056 (-132) (-279) (-207) (-075) (218) (-295) State Income Tax Rate 0055 0007 0006 0029 0004 0007 (314) (086) (038) (146) (024) (041) CEO Age -0017 -0025 -0023 -0070 -0154 -0078 (-103) (-422) (-153) (-397) (-863) (-463) High Salary 0360 -0009 0229 0107 -0086 -0003 (516) (-039) (332) (258) (-178) (-007) Total Wealth 0095 0904 0253 (220) (936) (244)

Observations 5916 5916 5916 5916 5916 5916 Adjusted R-squared 0386 0866 0371 0271 0197 0311 Partial R-squared 00247 0604 00569 00138 00289 000953 Partial F-statistic 1216 2405 452 1186 1115 1127 p-value 0014 0004 0081 0015 0017 0017

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

58

Table 8 continued Second-stage estimates Second-stage estimates using unscaled incentive variables are shown in Panel B and scaled incentive variables in Panel C Incentive variables instruments and controls (untabulated in Panels B and C) are measured in year t The risk choices are measured in year t+1 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively In Panels B and C we report coefficient estimates in bold face if they are significant based on Anderson-Rubin (1949) robust 95 confidence intervals

Panel B Second-stage estimates using unscaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega 0021 1007 -0196

(023) (627) (-254) Total Sensitivity 0419 1019 0241

(405) (475) (213)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0488 0273 0466 0465 0274

Average coefficient 0277 0560 t-statistic 432 514

Difference in avg coef 0283 t-statistic 424

Panel C Second-stage estimates using scaled incentive variables

ln(Stock

Volatility) RampD

Expense Book

Leverageln(Stock

Volatility) RampD

Expense Book

Leverage (1) (2) (3) (4) (5) (6)

Vega Total Wealth -0087 0876 -0346

(-064) (616) (-259) Tot Sensitivity Tot Wealth 0280 0833 0152

(180) (581) (166)

Observations 5916 5555 5511 5916 5555 5511 Adjusted R-squared 0462 0506 0283 0464 0472 0279

Average coefficient 0147 0423 t-statistic 226 475

Difference in avg coef 0274 t-statistic 390

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

59

Table 9 Comparison of the association between changes in vega and changes in equity sensitivity and changes in volatility RampD and leverage around the introduction of SFAS 123R This table presents OLS regression results using the change in unscaled (Panel A) and scaled (Panel B) incentive variables Incentive variables and controls (untabulated) are the difference between the mean from 2005 to 2008 and the mean from 2002 to 2004 following Hayes et al (2012) The dependent variables are the difference between the mean from 2006 to 2009 and the mean from 2003 to 2005 The incentive variables are described in detail in Appendix A Control and dependent variables are described in Appendix B The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Change in unscaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega -0038 -0004 -0017

(-127) (-014) (-058) Δ Equity Sensitivity -0036 0014 0145

(-113) (065) (495)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 00587 00351 0109 00587 00353 0128 Average coefficient -0020 0041 t-statistic -119 240 Difference in avg coef 0061 t-statistic 395

Panel B Change in scaled incentive variables

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

Δ ln(Stock Volatility)

Δ RampD Expense

Δ Book Leverage

(1) (2) (3) (4) (5) (6) Δ Vega Total Wealth 0035 0012 -0005

(096) (031) (-011) Δ Equity Sens Total Wealth 0074 -0005 0247

(191) (-013) (661)

Observations 1168 1131 1106 1168 1131 1106 Adjusted R-squared 0138 00312 0109 0140 00312 0147 Average coefficient 0014 0105 t-statistic 066 505 Difference in avg coef 0091 t-statistic 573

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760

60

Table 10 Comparison of the association between vega and equity sensitivity adjusted for long-term incentive award convexity and future volatility RampD and leverage This table presents OLS regression results using unscaled (Panel A) and scaled (Panel B) incentive variables adjusted to include the estimated convexity from long-term incentive awards Incentive variables and controls (untabulated) are measured in year t The dependent variables are measured in year t+1 The incentive variables are described in detail in Appendix A and adjusted for the convexity of long-term incentive awards Control and dependent variables are described in Appendix B Total wealth is also adjusted by the value of long-term incentive awards All regressions include year and 2-digit SIC industry fixed effects The t-statistics reported in parentheses are based on robust standard errors clustered by both firm and year and indicate significance at the 1 5 and 10 levels respectively

Panel A Unscaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adjusted Vega -0066 0157 -0071

(-205) (607) (-374) Adjusted Total Sensitivity 0014 0101 0124

(058) (473) (507)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0464 0405 0274 0462 0396 0281

Average coefficient 0007 0080 t-statistic 071 908

Difference in avg coef 0073 t-statistic 882

Panel B Scaled Incentive Variables

ln(Stock

Volatility) RampD

Expense Book

Leverage ln(Stock

Volatility)RampD

ExpenseBook

Leverage (1) (2) (3) (4) (5) (6)

Adj Vega Adj Tot Wealth 0057 0249 0090 (216) (772) (255)

Adj Tot Sens Adj Tot Wealth 0165 0175 0344 (547) (469) (722)

Observations 5940 5560 5513 5940 5560 5513 Adjusted R-squared 0491 0423 0275 0504 0406 0343

Average coefficient 0132 0228 t-statistic 668 830

Difference in avg coef 0099 t-statistic 760