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ESSAYS ON CORPORATE RISK GOVERNANCE
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL OF BUSINESS
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Gaizka Ormazabal
June 2011
http://creativecommons.org/licenses/by/3.0/us/
This dissertation is online at: http://purl.stanford.edu/hp926sh2992
© 2011 by Gaizka Ormazabal Sanchez. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution-3.0 United States License.
ii
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
David Larcker, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Mary Barth
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Madhav Rajan
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Stefan Reichelstein
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.
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ABSTRACT
This dissertation comprises three papers on the governance of corporate risk:
1. The first paper investigates the role of organizational structures aimed at
monitoring corporate risk. Proponents of risk-related governance
structures, such as risk committees or Enterprise Risk Management (ERM)
programs, assert that risk monitoring adds value by ensuring that corporate
risks are managed. An alternative view is that such governance structures
are nothing more than window-dressing created in response to regulatory
or public pressure. Consistent with the former view, I find that, in the
period between 2000 and 2006, firms with more observable risk oversight
structures exhibit lower equity and credit risk than firms with fewer or no
observable risk oversight structures. I also provide evidence that firms
with more observable risk oversight structures experienced higher returns
during the worst days of the 2007-2008 financial crisis and were less
susceptible to market fluctuations than firms with fewer or no observable
risk oversight structures. Finally, I find that firms without observable risk
oversight structures experienced higher abnormal returns to recent
legislative events relating to risk management than firms with observable
risk oversight structures.
2. The most common empirical measure of managerial risk-taking incentives
is equity portfolio vega (Vega), which is measured as the dollar change in
v
a manager’s equity portfolio for a 0.01 change in the standard deviation of
stock returns. However, Vega exhibits at least three undesirable features.
First, Vega is expressed as a dollar change. This implicitly assumes that
managers with identical Vega have the same incentives regardless of
differences in their total equity and other wealth. Second, the small change
in the standard deviation of returns used to calculate Vega (i.e., 0.01)
yields a very local approximation of managerial risk-taking incentives. If
an executive’s expected payoff is highly nonlinear over the range of
potential stock price and volatility outcomes, a local measure of incentives
is unlikely to provide a valid assessment of managerial incentives. Third,
Vega is measured as the partial derivative of the manager’s equity
portfolio with respect to return volatility. This computation does not
consider that this partial derivative also varies with changes in stock price.
The second paper develops and tests a new measure of managerial risk-
taking equity incentives that adjusts for differences in managerial wealth,
considers more global changes in price and volatility, and explicitly
considers the impact of stock price and volatility changes. We find that
our new measure exhibits higher explanatory power and is more robust to
model specification than Vegafor explaining a wide range of measures of
risk-taking behavior.
3. The third paper examines the relation between shareholder monitoring and
managerial risk-taking incentives. We develop a stylized model to show
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that shareholder monitoring mitigates the effect of contractual risk-taking
incentives on the manager’s actions. Consistent with the model, we find
empirically that the positive association between the CEO’s contractual
risk-taking incentives and risk-taking behavior decreases with the level of
shareholder monitoring. Furthermore, consistent with the board
anticipating and optimally responding to shareholder monitoring, boards
of firms exposed to more intense monitoring design compensation
contracts that provide higher incentives to take risks. Overall, our results
suggest that, when evaluating risk-taking incentives provided by a
compensation contract, it is important to account for the firm’s monitoring
environment.
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ACKNOWLEDGMENTS
I thank especially my advisor, David Larcker, for his continuous advice and
support, and for so many coffees and fun conversations. I also thank the other members
of my dissertation committee, Mary Barth, Madhav Rajan, and Stefan Reichelstein for
advice and encouragement, and for detailed comments on multiple versions of the
manuscript. I am also especially indebted to Dan Taylor for providing invaluable
feedback, advice, and friendship. I also thank Peter Reiss, Michael Klaussner, Andrey
Malenko, Alan McCall, Eric So, and Salman Arif for helpful comments, Ian Gow for
advice, Chris Armstrong for sharing code, and Governance Metrics, Inc. for sharing data.
Finally, I thank my parents, Kepa and Begoña, and my brothers Kepa and Gilen,
for all of their support. I am also grateful to all the friends I have made during these
years, especially Anthony, Matt, Pat, Alan, Jim, Victor, Miguel, Torlach, Tim, Ed, Tom,
Juan, Jun, Justin, and Allen (among many others). Eskerrik asko guztioi, bihotz-bihotzez
(which is Basque for “a big thanks to all of you!”).
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TABLE OF CONTENTS
List of Tables ..................................................................................................................... xi
List of Figures .................................................................................................................... xi
Introduction ..........................................................................................................................1
Chapter 1: An Examination of Corporate Risk Oversight ...................................................5
1. Introduction ..............................................................................................................5
2. Background, Literature Review and Hypothesis Development ...............................8
2.1. Institutional Background ..............................................................................8
2.2. Literature Review.......................................................................................11
2.3. Hypothesis Development ...........................................................................13
3. Sample and Measurement Choices ........................................................................16
3.1. Data and Sample Description.....................................................................16
3.2. The Risk Oversight Index ..........................................................................17
3.3. Descriptive Statistics ..................................................................................18
4. Association Between Risk Oversight and Firm Risk .............................................20
4.1. Cross-Sectional Analysis Before The 2007-2008 Financial Crisis............20
4.1.1. Research Design.............................................................................20
4.1.2. Results ............................................................................................24
4.2. Time Series Analysis Before the 2007-2008 Financial Crisis ...................26
4.2.1. Research Design.............................................................................26
4.2.2. Results ............................................................................................27
4.3. Stock Market Performance during the 2007-2008 Financial Crisis...........28
4.3.1. Research Design.............................................................................28
4.3.2. Results ............................................................................................30
5. Stock Market Reaction to Legislation Related to Risk Oversight .........................31
5.1. Research Design.........................................................................................31
5.2. Results ........................................................................................................35
ix
6. Sensitivity Analyses ...............................................................................................38
6.1. Additional Control Variables .....................................................................38
6.2. Alternative Measurement of Key Variables ..............................................39
6.3. Endogeneity and Model Misspecification .................................................40
6.3.1. Obtaining Matched Pairs................................................................41
6.3.2. Differences in Risk Between Matched Pairs .................................42
6.3.3. Sensitivity to Hidden Bias .............................................................42
7. Conclusion .............................................................................................................44
Chapter 2: Measuring Risk-Taking Incentives ..................................................................46
1. Introduction ............................................................................................................46
2. Equity Portfolio Risk Elasticity .............................................................................51
3. Sample and Variable Measurement .......................................................................57
4. Empirical Analysis of Risk Elasticity ....................................................................61
4.1. Risk-Taking Incentives and Equity Risk ...................................................61
4.1.1. Future Stock Return Volatility .......................................................62
4.1.2. Future Idiosyncratic and Systemic Risk ........................................65
4.2. Risk-Taking Incentives and Credit Risk ....................................................66
4.3. Risk-Taking Incentives and Alternative Measures of Risk-Taking
Behavior ...........................................................................................................69
4.3.1. Extreme Stock Returns ..................................................................69
4.3.2. Implied Stock Return Volatility .....................................................71
4.3.3. Research and Development Expenditures .....................................72
5. Sensitivity Analyses ...............................................................................................73
5.1. Sensitivity to Hidden Bias and Linearity Assumptions .............................74
5.2. Sensitivity to Model Specification and Functional Form ..........................79
5.3. Sensitivity to Variations of Risk Elasticity Calculation ............................83
6. Conclusions ............................................................................................................88
Chapter 3: Shareholder Monitoring and Risk-Taking Incentives ......................................92
x
1. Introduction ............................................................................................................92
2. Theory and Empirical Predictions .........................................................................98
2.1. Model Setup ...............................................................................................98
2.2. Risk-Taking for a Given Compensation Scheme .....................................102
2.3. Endogenous Monitoring and Compensation ............................................104
2.4. Empirical Predictions ...............................................................................107
3. Data and Empirical Approach ..............................................................................109
3.1. Sample and Variable Construction ..........................................................109
3.2. Research Design.......................................................................................111
4. Empirical Results .................................................................................................114
5. Robustness ...........................................................................................................117
5.1. Matched Pair Design ................................................................................117
5.2. Other Robustness Checks ........................................................................122
6. Conclusion ...........................................................................................................124
Appendix A: Variable Definitions ...................................................................................125
Appendix B: The Risk Oversight Index...........................................................................127
Appendix C: Legislative Events Related To Risk Oversight ...........................................129
Appendix D: Figures ........................................................................................................130
Appendix E: Proofs ..........................................................................................................132
Appendix F: Tables ..........................................................................................................134
Bibliography ....................................................................................................................166
xi
LIST OF FIGURES
Number Page
Figure 1: Graphical Depiction of Equity Portfolio Risk Elasticity ..................................130
Figure 2: Examples of Risk Elasticity .............................................................................131
xii
LIST OF TABLES
Number Page
Table 1: Descriptive Statistics .........................................................................................134
Table 2: Association Analysis Before the 2007-2008 Financial Crisis ...........................136
Table 3: Time-series Analysis Before the 2007-2008 Financial Crisis ...........................139
Table 4: Stock Market Performance During the 2007-2008 Financial Crisis .................140
Table 5: Market Reaction to Legislation Related to Risk Oversight ...............................141
Table 6: Propensity-score Matched Pair Analysis ...........................................................143
Table 7: Descriptive Statistics .........................................................................................145
Table 8: Risk-taking Incentives and Equity Risk ............................................................147
Table 9: Risk-taking Incentives and Credit Risk .............................................................150
Table 10: Alternative Measures of Risk-taking Behavior ...............................................152
Table 11: Propensity-score Matched Pair Analysis .........................................................155
Table 12: Robustness to Model Specification and Functional Form ...............................157
Table 13: Variations of the Risk Elasticity calculation ...................................................159
Table 14: Descriptive Statistics .......................................................................................160
Table 15: Shareholder Monitoring and the effect of Risk-taking Incentives...................161
Table 16: Risk-taking Incentives and Shareholder Monitoring .......................................163
Table 17: Propensity-score Matched Pair Analysis .........................................................164
1
INTRODUCTION
The primary theme of my work is the governance of corporate risk. I approach
corporate risk governance from two perspectives: monitoring and incentives. There is a
growing literature in finance and accounting that examines which corporate governance
practices affect outcomes important to investors. Another stream of the corporate finance
literature examines the economic rationale for managing firm risk. However, there is still
much to learn about the way firms govern their risk, namely how companies monitor
their risks and design compensation schemes to induce optimal risk-taking behavior.
Because corporate governance and risk management are at the heart of the debate on the
2007-2008 financial meltdown, this novel line of research is relevant not only to
academics, but also to regulators and market participants.
Some related literature examines the economic determinants and performance
consequences of using financial derivatives. Specifically, several studies empirically test
whether financial hedging can increase firm value. Other studies address the question of
whether derivatives are associated with firm risk. However, the existing literature does
not explore the mechanisms firms use to monitor their risks. Because the use of financial
derivatives is only part of the corporate risk management process and, like other
managerial actions, is subject to agency problems and imperfect information, analyzing
risk oversight practices is likely to shed new light to understand the value implications of
corporate risk management.
2
I investigate organizational risk oversight in the first chapter. In particular, I
examine whether risk oversight structures are window-dressing mechanisms intended to
bias investors’ perception of the firm’s riskiness or to meet legal or regulatory
requirements. Consistent with the idea that risk oversight structures are not mere
window-dressing mechanisms, I find that firms with risk oversight structures exhibit
lower equity and credit risk than firms without observable risk oversight structures, and
are less sensitive to the extreme market shocks that occurred during the 2007-2008
financial crisis. I also explore the value implications of risk oversight by examining the
equity market reaction to the introduction of corporate governance legislation that
proposed to require all firms to have specific risk oversight structures. I find a significant
difference in the market reaction for firms with and without risk oversight structures at
the time of the legislation. In particular, equity prices of firms without pre-existing risk
oversight structures responded more positively to these events than firms with such
structures. Assuming that markets are efficient, this result suggests that introducing risk
oversight structures can increase shareholder wealth.
Overall, the findings of the first chapter suggest that risk oversight structures are
not window-dressing mechanisms to avoid regulatory or public pressure. Instead, the
evidence indicates that firms with risk oversight structures exhibit lower risk, and that
risk oversight can increase shareholder value.
Another stream of literature in finance and accounting explores how executives
respond to risk-taking incentives and find an empirical association between risk-taking
incentives and some risk-taking actions. However, if we are to understand whether risk-
3
taking incentives are optimally designed, there is still much to learn about how and
whether risk-taking incentives map into specific risk-taking actions and how these actions
translate into firm risk. An important stepping stone in this regard is the measurement of
risk-taking incentives. The most common empirical measure of managerial risk-taking
incentives is equity portfolio vega, which is measured as the dollar change in a manager’s
equity portfolio for a 0.01 change in the standard deviation of stock returns. However,
vega exhibits several undesirable features. The second chapter, coauthored with
Christopher Armstrong and David Larcker, develops and tests a new measure of
managerial risk-taking equity incentives that adjusts for differences in managerial wealth,
considers more global changes in price and volatility, and explicitly considers the impact
of stock price and volatility changes. We find that our new measure exhibits higher
explanatory power and is more robust to model specification than vega for explaining a
wide range of measures of risk-taking behavior.
Finally, the third chapter, coauthored with Andrey Malenko, analyzes a setting in
which risk monitoring and risk-taking incentives interact, and propose risk monitoring as
a new explanation for the observed differences in risk-taking incentives across firms.
Specifically, we posit that shareholder monitoring can mitigate the effect of contractual
risk-taking incentives on the manager's actions. We also show that, anticipating this
behavior, boards of firms exposed to more intense monitoring design compensation
contracts providing higher incentives to take risks. Consistent with these theoretical
predictions, we find empirically that the positive association between the CEO's
contractual risk-taking incentives and risk-taking behavior decreases with the level of
4
shareholder monitoring. Finally, we also document that firms exposed to more intense
monitoring design compensation contracts providing higher incentives to take risks.
Overall, our results suggest that, when evaluating risk-taking incentives provided by a
compensation contract, it is important to account for the firm's monitoring environment.
Collectively, the evidence in this dissertation suggests that the governance of
corporate risk, either in the form of monitoring (chapters one and three) or incentives
(chapters two and three), shapes managerial decision making and translates into
observable outcomes.
5
CHAPTER 1: AN EXAMINATION OF CORPORATE RISK OVERSIGHT
1. INTRODUCTION
This paper analyzes the role of organizational structures aimed at monitoring
corporate risk. The economic upheaval following the recent financial crisis has given rise
to the idea that, beyond the use of derivatives for hedging purposes, companies should
monitor their risks more closely.1 Specifically, some commentators argue that the board
should take the necessary steps to “set the tone and culture towards effective risk
management” throughout the organization (e.g., COSO, 2009). Throughout the paper, I
refer to the organizational effort to monitor corporate risk as “risk oversight”.2 Using
data on risk oversight practices of US public firms, this paper examines whether risk
oversight is related to risk and shareholder value. I find that risk oversight is negatively
related to risk and positively related to shareholder value.
Previous literature shows that risk management can add value in the presence of
frictions such as taxation, bankruptcy costs, costly external finance, information
asymmetry, and managerial risk aversion. While some studies examine the determinants
and value implications of the use of financial derivatives, other potentially important
dimensions of risk management, such as risk oversight, remain unexplored.
1 See for example Senator Reed’s speech during the Senate hearing on 3/18/2009
(http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=111_senate_hearings&docid=f:52966.pdf )
and Chairman Bernanke’s speech during the Senate hearing on 12/3/2009
(http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=111_senate_hearings&docid=f:54239.pdf).
For survey evidence supporting this view see, for example, The Economist’s 2009 “Beyond Box Ticking:
A new era for risk governance” study and Accenture’s 2009 “Global Risk Management” study, among
others. 2 “Risk oversight” is the term used in the recent SEC rule on proxy disclosure enhancements
(http://www.sec.gov/rules/final/2009/33-9089.pdf).
6
This paper hypothesizes that risk oversight leads to lower risk, and that risk
oversight can add value. Alternatively, risk oversight structures could be window-
dressing mechanisms to avoid regulatory pressure or public scrutiny. For example, risk
oversight structures could be adopted to avoid accusations of breach of fiduciary duty, to
comply with regulation such as Sarbanes-Oxley, or to meet listing requirements. In that
case, risk oversight would be unrelated to firm risk, and would not increase shareholder
value.
My measure of the effort that an organization exerts to oversee its risks is an
index constructed using publicly observable data on five risk oversight structures: (i) risk
committee, (ii) Enterprise Risk Management (ERM), (iii) existence of a Chief Risk
Officer (CRO) or similar position, (iv) policy and standards related to risk management,
and (v) other organizational structures related to risk oversight.
I first explore the relation between the risk oversight index and equity and credit
risk. I find evidence that risk oversight is negatively associated with both equity and
credit risk. Specifically, the risk oversight index shows a robust negative association
with idiosyncratic volatility and systematic risk. I repeat the analysis using two measures
of credit risk: spreads from private loans and credit ratings. Consistent with the idea that
risk oversight serves not only shareholders, but also debtholders, I find that the risk
oversight index is negatively associated with loan spreads and positively associated with
credit ratings.
To mitigate self-selection concerns related to the negative association between
risk oversight and risk, I analyze whether that association holds not only in the cross-
7
section, but also in the time series. I find that the implementation of risk oversight
structures is associated with a decrease in future equity and credit risk.
Next, to examine whether oversight mitigates the effect of systemic shocks, I test whether
firms that had different levels of risk oversight before 2007 experienced different stock
market performance during the 2007-2008 financial crisis. I find that firms with higher
levels of risk oversight were less susceptible to fluctuations in stock market returns and
experienced higher returns during the recent financial crisis, when stock prices
experienced the largest declines.
Finally, I explore the value implications of risk oversight by examining the equity
market reaction to the introduction of corporate governance legislation that proposed to
require all firms to have specific risk oversight structures. I find a significant difference
in the market reaction for firms with and without risk oversight structures at the time of
the legislation. In particular, equity prices of firms without pre-existing risk oversight
structures responded more positively to these events than firms with such structures.
Assuming that markets are efficient, this result suggests that introducing risk oversight
structures can increase shareholder wealth.
Collectively, the results support the notion that risk oversight structures are more
than mere window-dressing mechanisms. However, because the need for risk oversight
can vary significantly in the cross-section, I do not interpret these results as advocating a
specific form of risk oversight for all firms.
The remainder of the paper proceeds as follows. Section 2 provides background
information about risk oversight, discusses the related prior literature, and develops the
8
main hypothesis of the paper. Section 3 discusses the sample and the measurement of
key variables. Section 4 presents tests of the association between risk oversight and firm
risk. Section 5 presents tests of the stock market reaction to legislative events related to
risk oversight. Section 6 discusses the sensitivity tests, and section 7 concludes.
2. BACKGROUND, LITERATURE REVIEW AND HYPOTHESIS DEVELOPMENT
2.1. INSTITUTIONAL BACKGROUND
The last decade has seen an increase in regulation that relates to the risk
management responsibilities of corporate officers and directors. First, recent state law
jurisprudence implies that failure to ensure that the risks faced by the company are
understood and managed in the best interest of shareholders could be considered a breach
of duty.3 Second, both in the U.S. and internationally, there is a growing body of law and
regulation related to risk management: Sarbanes-Oxley, the Federal Sentencing
Guidelines, and other laws and regulations related to issues such as fraudulent conduct by
employees, product liability, health and safety, and environmental compliance.4 Third,
3 The Business Judgment Rule is often cited as the main standard of review of director conduct by
Delaware courts. In re Caremark International Inc. Derivative Litigation, 698 A.2d 959, 971 (Del. Ch.
1996) the Delaware Chancery Court stated that director liability for a failure of board oversight required a
sustained or systemic failure of the board to exercise oversight, such as an utter failure to assure a
reasonable information and reporting system exists, and noted that this was a “demanding test”. However,
more recent jurisprudence revises the definition of the duty of good faith (in re Walt Disney Co.Derivative
Litig., Cons. C.A. No. 15452, 2005 Del. Ch. LEXIS 113 (Del Ch. Aug. 9, 2005)). While upholding the
validity of the Business Judgment Rule, Chancellor Chandler underscored the importance of good faith in
the performance of corporate duties and stated that directors and officers are expected to fully understand
current best practices (such as risk management) as well as ensure that business decisions are taken in light
of widely recognized corporate governance standards. 4 Among other things, Sarbanes-Oxley introduced the SOX 404 top-down risk assessment of
management’s testing of its internal controls. Amendments to the Federal Sentencing Guidelines (effective
as of November of 2004) provide for a more lenient treatment of corporate crimes if the organization had
established a well-functioning and qualifying compliance program (see Chapter Eight (“Sentencing of
9
some stock exchanges now include explicit risk oversight requirements for all listed
companies.5 Fourth, following the Troubled Asset Relief Program (TARP) contained in
the Emergency Economic Stabilization Act of 2008, some U.S. congressmen and senators
introduced legislation with provisions focused on risk management. This legislation
included the Shareholder Bill of Rights Act of 2009, introduced in the U.S. Senate on
May 19, 2009, and the Corporate Governance Reform Act of 2009, introduced in the U.S.
House of Representatives on July 21, 2009. The proposed legislation would require that,
among other things, all public companies establish a risk committee composed entirely of
independent directors.6 Although these bills were not passed in their initial form, their
content was included with some modifications in the recently approved Financial Reform
Act of 2010. Finally, the Securities and Exchange Commission (SEC) recently issued a
new disclosure requirement on “the extent of the board’s role in the risk oversight of the
company.”7
Organizations”), Amendment 673 (Supplement to Appendix C) 2004 Federal Sentencing Guidelines
Manual). 5 New York Stock Exchange (NYSE) Corporate Governance Rules recently were changed to include
explicit requirements for NYSE registrant audit committees to assume specific responsibilities with respect
to risk assessment and risk management, including risks beyond financial reporting (see Section 303A of
the NYSE Listing Manual). 6 First, Senator Schumer introduced the Shareholder Bill of Rights Act of 2009 into the U.S. Senate on May
19, 2009, which proposed to require that, among other things, all public companies establish a “risk
committee” composed entirely of independent directors. Subsequently, Senator Ellison introduced the
Corporate Governance Reform Act of 2009 into the U.S. House of Representatives on July 21, 2009. If
passed, this bill would have required that all public companies create an independent risk management
committee “established by and amongst the board of directors of an issuer for the purpose of overseeing the
risk management policies and procedures of the issuer” and appoint a Chief Risk Officer who shall “(1)
establish, evaluate, and enforce the risk management policies and procedures of the issuer; and (2) report
directly to the risk management committee.”
7 According to the SEC rule issued in February 2010, this disclosure about the board’s approach to risk
oversight “should address questions such as whether the persons who oversee risk management report
directly to the board as a whole, to a committee, such as the audit committee, or to one of the other standing
committees of the board; and whether and how the board, or board committee, monitors risk” (see Final
Rule on “Proxy Disclosure Enhancements” (http://www.sec.gov/rules/final/2009/33-9089.pdf)).
10
In recent years, the risk oversight function has been implemented through several
mechanisms: (i) establishing a board-level risk committee (RC), (ii) appointing a Chief
Risk Officer (CRO), (iii) implementing an Enterprise Risk Management (ERM) program,
(iv) adopting risk-management policies or standards, and (v) assigning the risk oversight
function (or part of it) to an existing board committee.8 First, in the charters of the risk
committees or other committees entrusted with risk oversight, boards are held responsible
for ensuring that management understands the risks that the company is facing and is
taking the appropriate actions to minimize or transfer such risks. Second, the CRO or
similar position entails independent accountability to the executive committee and the
board on the quality of enterprise-wide risk management. Finally, the ERM framework
and recent risk management standards emphasize the leadership role of the board and
senior executives in risk management.9
Survey evidence suggests that market participants’ interest in risk oversight is
growing. First, recent industry-specific guidance and general best practices manuals
support the notion that risk management and governance should be linked.10
Second,
8 In small companies, the risk committee is often substituted by a review of risk management as a
dedicated, periodic agenda item for an existing committee such as the audit committee, in addition to
periodic review by the board (Kendall, 1998). In contrast, some large companies have more than one risk
committee, one at the board level and another (or several others) at the top management or divisional level.
Recent survey data suggests, however, that a significant number of boards are shifting responsibility for
risk oversight away from audit committees to risk committees, because the audit committee is overtasked
(see www.AgendaWekk.com, April 19, 2010).
9 COSO defines ERM as "[a] process, effected by an entity’s board of directors, management and other
personnel, applied in strategy setting and across the enterprise, designed to identify potential events that
may affect the entity, and manage risk to be within its risk appetite, to provide reasonable assurance
regarding the achievement of entity objectives" (COSO, 2004). The upcoming International Standard ISO
31000 gives principles and guidelines for the implementation of risk management programs emphasizing
that risk management should improve corporate governance.
10 See, for example, the Committee of Sponsoring Organizations of the Treadway Commission (COSO),
several guidelines specifically oriented to the banking industry, other industry-specific guidelines (for
11
Enterprise Risk Management (ERM) has given rise to an industry of ERM-related
consulting services, software, courses, and research centers, suggesting that there is a
demand for these services. Third, the media attention devoted to ERM in recent years
and the number of times it appears in SEC filings and conference calls also shows an
increase in interest.11
Fourth, credit rating agencies recently started to incorporate ERM
criteria in their ratings.12
Finally, survey data suggest that an increasing number of
executives see ERM as a way to potentially increase shareholder value. However,
despite this apparent increased attention, survey data also indicate that, before 2007,
ERM implementation was limited (The Corporate Board, 2007).
2.2. LITERATURE REVIEW
Prior literature identifies conditions under which risk management can add value
to diversified investors. This literature departs from a perfect world in which risk
management does not have a role in maximizing shareholder wealth (e.g. Modigliani and
Miller, 1958, 1961) and justifies the existence of financial risk management as derived
from violations of the perfect world assumptions. Specifically, previous work has
justified the use of risk management by the existence of taxes (e.g. Smith and Stulz,
1985; Nance et al, 1993), financial distress costs (Smith and Stulz, 1985), external
financing and investment opportunities (e.g., Froot et al., 1993; Geczy et al.,1997),
utilities, ports, nuclear materials management, and pharmaceuticals), and corporate governance guidelines
of foreign jurisdictions such as the Turnbull Report in the UK.
11 A casual search on Factiva reveals a steady increase in the number of times the words "Enterprise Risk
Management (ERM)" appears in the news (185 hits in 2000, 1,358 hits in 2006, and 2,771 hits in 2009). In
terms of public disclosures, ERM appears in 67 SEC filings in 2000, 768 SEC filings in 2006 and 1,391
SEC filings in 2009 (usually proxy statements, 10-K or 10-Q reports). 12
http://www2.standardandpoors.com/portal/site/sp/en/us/page.topic/ratings_erm
12
agency costs (e.g., DeMarzo and Duffie, 1991), owners’ risk aversion, and agency
problems with other stakeholders (Stulz, 1996).
Based on this theoretical literature, several studies empirically test the
performance consequences of derivatives use. Some studies test whether financial
hedging can increase firm value (e.g., Allayannis and Weston, 2001; Carter, Rogers, and
Simkins, 2004). More recently, Mackay and Moeller (2007) use a sample of 34 oil
refiners to show that corporate risk management can add to firm value. The conclusions
of these studies generally support the notion that financial hedging adds value to
shareholders. However, given the endogenous nature of risk management and the
difficulty of testing cross-sectional differences in firm value, the results of these papers
should be interpreted cautiously.13
Moreover, the results of these studies are usually
limited to a specific industry or type of derivative.
Other studies address the question of whether derivatives are associated with firm
risk. Specifically, Guay (1999b) finds that firm risk declines following derivative use for
a sample of new users of derivatives. Schrand (1998) and Wong (2000) find an
association between interest rate and foreign exchange sensitivities and disclosures about
derivative instruments. Despite this evidence in support of the use of derivatives, Guay
and Kothari (2003) cast doubt on the importance of the role of derivatives held by non-
financial firms. Specifically, Guay and Kothari (2003) simulate the amounts that the
firms would collect in the case of extreme fluctuations of interest rates, currency
13
These papers generally use Tobin’s Q as a proxy for firm value. Although this is a common practice in
the literature, it is well known that Tobin’s Q is also used as a proxy for other things, such as investment
opportunities.
13
exchange rates, and security prices, and find that those amounts are modest relative to
key firm characteristics such as size and operating cash flow. Although these studies
provide insight into the role of derivatives in mitigating risk, they do not address risk
monitoring.
2.3. HYPOTHESIS DEVELOPMENT
The null hypothesis of this paper is that observed risk oversight structures are
window-dressing mechanisms intended to bias investors’ perception of the firm’s
riskiness or to meet legal or regulatory requirements. For example, directors and officers
could implement risk oversight structures to avoid being accused of breaching their
fiduciary duties, to meet NYSE requirements, to obtain a more lenient punishment for
corporate crimes under the Federal Sentencing Guidelines, to meet legal requirements
(e.g., TARP or the Financial Reform Act of 2010), or to meet recent SEC disclosure
requirements (see section 2.1 for a detailed explanation of recent legal and regulatory
developments related to risk management). Anecdotal evidence suggests it is plausible
that, in practice, risk oversight structures have little or no impact on shareholder value.14
Alternatively, it is also possible that risk oversight translates into a better
understanding of corporate risks and value-enhancing risk-taking. As explained by
Nocco and Stulz (2006), optimizing the risk-return tradeoff can be done in two ways.
First, a firm that has no special ability to bear a particular risk (i.e., “non-core” risk)
14
For example, Standard & Poor’s recent report on enterprise risk management practices points out that
“few companies demonstrated that their risk management would help them tremendously in staving off
future financial loss or seize opportunities their competitors could miss” (see www.AgendaWeek.com,
August 10, 2009). Other occasional anecdotal evidence also suggests that, even though some companies
have risk management systems in place, those systems are still not an integral component of decision
making (see, for example, http://cebviews.com/2010/03/risky-business-what-leading-risk-managers-are-
talking-about/)
14
should reduce (or eliminate) that risk. Second, the firm should retain those risks for
which it has a comparative advantage in risk-bearing (i.e., “core” risks). In other words,
“non-core” (“core”) risks are suboptimal (optimal) in terms of risk-return trade-off and
the risk “appetite” of the firm (i.e., the optimal probability of financial distress), and
should be transferred (retained). For example, insurance companies retain insurance risks
but hedge their exposures to interest rate risk. Thus, ex ante, the sign of the association
between risk oversight and risk is conditional on which of the two ways of optimizing the
risk-return tradeoff is more prevalent in practice. If risk oversight translates more
frequently into the identification and reduction of non-core risks, risk oversight and firm
risk should have a negative association. In contrast, risk oversight could lead to more
risk-taking when the firm identifies value-increasing business opportunities; namely, the
firm retains core risks (e.g., Schrand and Unal, 1998). Reducing non-core risks increases
the risk-taking capacity of the firm (i.e., the firm can take on more risk without incurring
distress costs) and enables it to take on more core risks. Thus, it is also possible that,
even when risk oversight is not window-dressing, we may not observe any association
between risk oversight and risk because the reduction in risk from transferring non-core
risks is offset by an increase in risk from retaining core risks.
These predictions are applicable to the association of risk oversight with both
idiosyncratic and systematic risk. The firm will optimize the risk-return relation,
aggregating both the systematic and idiosyncratic effect of the specific risk being
analyzed. Thus, the firm may decide to transfer (retain) a specific risk because it is non-
core (core) from either a systematic or an idiosyncratic point of view.
15
The association between risk oversight and credit risk is also conditional on
whether risk oversight is more related to reducing non-core risks than to retaining core
risks. If, in practice, risk oversight is mainly focused on reducing non-core risks, risk
oversight and credit risk should be negatively related, because reducing non-core risks
reduces the probability of distress. Alternatively, if risk oversight increases shareholder
value by retaining core risks without affecting the probability of financial distress, risk
oversight and credit risk should have no empirical association. Finally, risk oversight
could lead to the retention of risks that increase value for shareholders but also increase
the probability of financial distress (e.g., asset substitution). In this case, risk oversight
would be positively associated with credit risk.
Thus, the empirical prediction about the association between risk oversight and
both equity and credit risk depends on whether, in practice, risk oversight is more
frequently related to reducing non-core risks or to retaining core risks. Stated formally:
H1: If risk oversight translates more frequently into reduction of non-core
risks, then risk oversight is negatively associated with idiosyncratic risk,
systematic risk, and credit risk.
Regardless of whether risk oversight is more frequently associated with reducing
non-core risks than with retaining core risks, risk oversight could increase shareholder
value as long as its monitoring cost is lower than the benefits from optimizing the amount
of risk borne by the firm. Also, finding a negative association between risk oversight and
risk would be a sufficient condition to reject the null hypothesis that risk oversight is a
window-dressing mechanism, but would not be a sufficient condition to conclude that
risk oversight is value-increasing. For example, a reduction in firm equity volatility
16
could be suboptimal for shareholders if it reflected an agency conflict between directors
and shareholders, or between officers and shareholders. Thus, I test a second hypothesis
that relates to whether risk oversight can increase shareholder value. Stated formally:
H2: Risk oversight increases shareholder value.
3. SAMPLE AND MEASUREMENT CHOICES
3.1. DATA AND SAMPLE DESCRIPTION
The initial sample consists of 1,701 public firms for which data on risk oversight
practices were collected until June 2009 by GovernanceMetrics International, Inc. (GMI),
a leading corporate governance research and ratings firm. All the GMI data were
collected from public sources (SEC filings and corporate websites). The data include
information on five risk oversight practices: (i) the existence and characteristics of a risk
management committee, (ii) whether someone in the company is tasked with risk
management functions, (iii) whether the company makes disclosures on Enterprise Risk
Management (ERM), (iv) whether the company follows a risk management standard, and
(v) other organizational characteristics related to risk oversight. Specifically, the dataset
includes 25 dichotomous variables that relate to these five risk oversight practices (see
appendix B). I complement these data by searching SEC filings for the fiscal year in
which the risk oversight structures were implemented. For cases in which the
implementation date is not explicitly mentioned in the SEC filings, I assume that the year
of implementation is the first fiscal year in which those risk oversight structures appear in
the company’s disclosures.
17
I collect data on daily stock returns from the CRSP Quarterly Update daily stock
file and accounting data from Compustat. Additionally, the empirical tests require data
on executive compensation and institutional ownership. I collect data on executive
compensation from Equilar Inc. The Equilar file contains detailed information about
executive compensation for all but 12 firms in the sample. Data on institutional
ownership are collected from the Thomson-Reuters database of 13-F filings, otherwise
known as CDA/Spectrum. The Spectrum data file contains information on quarterly
institutional holdings for all institutional investors with $100 million or more under
management. Requiring institutional ownership data does not introduce any sample
attrition. The intersection of these datasets results in 1,689 firms and a total of 13,538
firm-year observations from 2000 to 2008.
3.2. THE RISK OVERSIGHT INDEX
I measure the degree of risk oversight in each firm by combining the 25 variables
in the GMI dataset into an index that is a proxy for the risk monitoring intensity in the
firm. The construction of the risk oversight index (ROindex) parallels the governance
index in Gompers et al. (2003), in that, for each firm, I add the value of the 25
dichotomous variables. The construction of this index relies on the assumption that each
of the 25 variables increases the intensity of risk oversight.
With the implementation dates for each of the five types of risk oversight
structures, I construct a time-variant index that reflects the number of risk oversight
structures that the company had implemented as of the end of a particular fiscal year. I
also construct five subindexes for the five types of risk oversight structures (see appendix
18
B). First, I construct a Risk Committee Index (RCindex) by adding the dichotomous
variables related to the firm’s risk committee. Similarly, I define three binary indicators
that take value of 1 if the company has, respectively, an ERM program (ERM), a policy
or standards following COSO (2004) or similar guidelines (COSO), and if a CRO or
similar position exists (CRO), and 0 otherwise. Finally, I define an index that adds the
data items related to other organizational structure related to risk monitoring (Other).
3.3. DESCRIPTIVE STATISTICS
Table 1 presents descriptive statistics for the sample. Panel A shows that the
sample spans the main sectors of the economy. Although there are many financial firms
among the 523 companies with risk oversight structures, 372 of those firms are not in the
financial industry. Panel A also reveals that entrusting the risk oversight function to an
existing committee of the board is the most common practice. However, 322 firms adopt
more specific risk oversight structures, such as risk committees at the board level, ERM
programs, CRO or similar position, or risk management standards.
Panel B reports the time series of adoption of risk oversight structures.
Specifically, panel B reports a significant increase in risk oversight in recent years,
probably as a consequence of the 2007-2008 financial crisis. However, even before the
recent financial crisis there was a steady increase in the risk monitoring practices. Panel
B also shows that there is substantial cross-sectional variation in ROindex across adopters
of risk oversight structures.
Panel C presents descriptive statistics for the variables used in the empirical tests
partitioned by firms that adopt risk oversight structures and firms that do not. Panel C
19
reveals that adopters are less risky. For example, the mean (median) idiosyncratic
volatility for firms with ROindex > 0 is 37% (31%), which is smaller than that of the non-
adopters (39% (34%)). Panel C also reveals that adopters tend to be larger, less
profitable, and more leveraged. Also, their executives receive more cash compensation
and have slightly more risk-taking incentives (Vega). Finally, panel C also shows that
adopters have fewer institutional investors in their ownership structure.
Comparing the firms covered by GMI with all firms on the CRSP/Compustat file
over the sample period reveals that both adopters and non-adopters are significantly less
risky than the median CRSP/Compustat firm. For example, panel C reveals that
idiosyncratic volatility for the median CSRP/Compustat firm is 46%, in contrast to that of
adopters (31%) and non-adopters covered by GMI (34%). Similarly, panel C also shows
that adopters and non-adopters covered by GMI are larger, more leveraged, more
profitable, have more institutional representation among their shareholders, and reward
their executives with higher levels of compensation and incentives than the median
CRSP/Compustat firm.
20
4. ASSOCIATION BETWEEN RISK OVERSIGHT AND FIRM RISK
4.1. CROSS-SECTIONAL ANALYSIS BEFORE THE 2007-2008 FINANCIAL CRISIS
4.1.1. Research Design
To test H1, I first examine the cross-sectional association between risk oversight
and measures of equity risk in the period before the 2007-2008 financial crisis, from 2000
to 2006.15
In particular, using OLS, I estimate equation (1).
EquityRiskt = δ0 + δ1 ROindext + δ2 Sizet + δ3 BMt + δ4 Leveraget +
δ5 ROAt + δ6 Returnt + δ7 IndustryVolt + δ8 PctInstitt +
δ9 CashCompt + δ10 Deltat + δ11 Vegat + δ12 Aget + εt. (1)
EquityRiskt is one of two proxies for equity risk in fiscal year t. The first is the logarithm
of the market-adjusted return volatility of the firm measured over the 250 trading days
before the firm’s fiscal year end (LogIdVol). This measure is a proxy for the firm’s
idiosyncratic risk.16
The second is the firm’s Beta as a measure of systematic risk
estimated as the coefficient of a regression of a firm’s daily returns on the market return
(adjusting both firm and market returns for the risk-free rate) over the 250 trading days
before the firm’s fiscal year end.
Regarding control variables, Size is the natural logarithm of equity market value
measured at the end of the fiscal year. BM is the equity book-to-market ratio. Leverage
is total liabilities scaled by total assets and ROA is operating income scaled by total
15
Including fiscal years 2007 and 2008 in the analysis could confound the results, because in those years
firms could have adopted risk oversight structures in response to the increase in systemic risk caused by the
2007-2008 financial turmoil.
16 I also repeat the analysis measuring idiosyncratic volatility as the standard deviation of the residuals in a
regression of daily returns on the market return over 250 days, and obtain similar results.
21
assets. Return is the daily stock return compounded over the 250 trading days before
fiscal year end. PctInstit is the percentage of shares owned by institutions. This set of
variables represents firm characteristics demonstrated in prior research to affect firm risk
(see e.g., Fama and French 1993, Ashbaugh et al., 2006). IndustryVol, defined as the
median return volatility for all the firms in the same 2-digit SIC code, is included to
control for industry affiliation.
Previous literature finds that some characteristics of compensation contracts are
associated with risk-taking behavior (e.g., Guay, 1999a; Rajgopal and Shevlin, 2002),
and agency problems (Core et al., 1999). Thus, equation (1) also includes control
variables related to managerial incentives and these characteristics. In particular, Delta
and Vega are the average risk-neutral sensitivities of the five highest-paid executives’
equity portfolios, estimated as in Core and Guay (2002). For each executive, Delta is the
increase in the value of the executive’s portfolio (in millions) for an increase of 1% in the
firm’s stock price. Vega is the increase in the value of the executive’s portfolio (in
millions) for an increase of 1% in the firm’s stock return volatility. CashComp is the
average annual cash compensation of the company’s five highest-paid executives. Age is
the average age of the company’s five highest-paid executives.17
To study the relation between risk oversight and the cost of debt, I estimate a
modified version of equation (1):
17
The results are not sensitive to using only Chief Executive Officer compensation variables or using the
median or maximum compensation of the top executives.
22
CreditRiskt = δ0 + δ1 ROindext + δ2 Sizet + δ3 BMt + δ4 Leveraget + δ5 ROAt +
δ6 Returnt + δ7 IndustryVolt + δ8 PctInstitt + δ9 CashCompt +
δ10 Deltat + δ11 Vegat + δ12 Aget + δ13 Volatilityt + εt. (2)
CreditRiskt is one of two proxies for credit risk for fiscal year t.18
First, I use the firm’s
average credit rating for fiscal year t (Rating). Rating ranges from 1 to 21, with 1
indicating the lowest rating and 21 indicating the highest rating. Because Rating is a
categorical variable, equation (2) is estimated using ordered logit. Second, because credit
ratings are subject to measurement error and to the incentives of the credit rating
agencies, I use private loan spreads as an alternative measure of the firm’s cost of debt.19
Specifically, I estimate equation (2) using the all-in-drawn spread charged by the bank
over LIBOR for the drawn portion of the loan facility (Allindrawn), and three additional
control variables: Dealamount, the loan amount, Maturity, the maturity period (in
months) of the loan, and Secured, an indicator variable that takes on the value 1 if loan
facility/bond is secured with collateral, and 0 otherwise. Volatility is the standard
deviation of daily returns measured over the 250 trading days before fiscal year end. The
rest of the variables are as previously defined.
Finally, I test whether risk oversight is associated with extreme operational and
market performance. This analysis is informative for two reasons. First, LogIdvol and
Beta do not inform about the tails of the cross-sectional distribution of performance,
namely whether a firm’s stock market and operational performance are more extreme in
18
I collect data on Standard and Poor’s (S&P) credit ratings from Compustat. Requiring non-missing credit
rating data produces 5,419 firm-year observations.
19 I collect data on private loans from the Dealscan database provided by Loan Pricing Corporation. The
intersection of the initial panel with Dealscan reduces the sample size to 3,720 firm-year observations.
23
absolute value than that of its peers. Second, analyzing the extremeness of the firm’s
operating profitability (ROA) allows me to investigate whether any association between
risk oversight and firm risk is attributable to operations or to investing and/or financing
activities. In particular, using a logit regression, I estimate a modified version of
equation (1):
ExtremeOutcomet = δ0 + δ1 ROindext + δ2 Sizet + δ3 BMt +
δ4 Leveraget + δ5 ROAt + δ6 Returnt + δ7 IndustryVolt +
δ8 PctInstitt + δ9 CashCompt + δ10 Deltat + δ11 Vegat +
δ12 Aget + δ13 Volatilityt + εt. (3)
ExtremeOutcomet is one of three measures of how extreme the firm’s performance is with
respect to the performance of its peers in fiscal year t. First, ExtremeRet is an indicator
variable that takes the value of 1 if the firm’s annual stock return lies in the top or bottom
quartile of the cross-sectional distribution of returns in that fiscal year, and 0 otherwise.
Second, ExtremeROA is a dichotomous variable taking the value of 1 if the firm’s
operating profitability (ROA) is in the top or bottom quartile of that fiscal year’s cross-
sectional distribution, and 0 otherwise. Finally, ExtremeROA is an indicator variable
taking the value of 1 if the firm’s future change in ROA (ROAt+1 – ROAt) is in the top and
bottom quartile of that fiscal year’s cross-sectional distribution, and 0 otherwise. The
correlations between these three variables and LogIdVol and Beta range from 9% to 31%,
suggesting that the former provide information about dimensions of risk not captured by
the latter. The rest of the variables in equation (3) are as defined in equations (1) and (2).
I focus my inferences on the sign and significance of the coefficient on ROindex.
The null hypothesis is that risk oversight structures are unrelated to firm risk, i.e., 1 = 0
24
in equations (1) through (3). Alternatively, if H1 is true and firm risk is significantly
lower for firms with more risk oversight structures, I predict 1 is negative in equations
(1) through (3).
Finally, to explore which types of risk oversight structures drive the association
with firm risk (if any), I estimate equations (1) through (3), substituting ROindex for the
five subindexes defined in section 3.2 (i.e., RCindex, ERM, RMstd, CRO and Other).
4.1.2. Results
Table 2, panel A, presents summary statistics from estimating equation (1). The
results in panel A show that ROindex has a significant association (p < 0.10, two-tail)
with the logarithm of idiosyncratic return volatility (LogIdVol) and with Beta. The
coefficient on ROindex is –0.01 when LogIdVol is the dependent variable (t-stat. of –
2.58). The significant coefficient of ROindex when Beta is the dependent variable (t-stat.
of –1.90) shows that risk oversight is associated with lower levels of idiosyncratic and
systematic risk. Panel B presents statistics analogous to those in panel A, but relating to
equation (2). The first set of columns presents statistics for the association between risk
oversight and proxies of cost of debt. Panel B reveals a significant association between
risk oversight and spreads charged by lenders in private debt contracts (t-stat. = –2.11).
Panel B also shows that risk oversight is positively associated with credit ratings (t-stat. =
1.72).
The results in panel C show that risk oversight is also negatively related to
extreme returns (t-stat. = –1.83), and extreme operational performance, both in terms of
ROA (t-stat. = –2.84) and future changes in ROA (t-stat. = –5.50). Because the results in
25
panels B and C hold after controlling for stock volatility, I infer that risk oversight is
associated not only with lower volatility, but also with probability distributions with
thinner tails.
Panel D presents results after decomposing ROindex into its components. The
last two columns show results partitioned by financial and non-financial firms. The first
two columns of panel D show that the negative association between risk oversight and
corporate risk is not attributable to a single type of risk oversight structure. Specifically,
the results reveal that risk committees, ERM programs, and risk management standards
are significantly negatively associated with return volatility (t-stat. of –2.53, –1.99, and –
1.67, respectively). The last two columns of panel D show that the negative association
between risk oversight and corporate risk holds for both financial and non-financial
firms.
Finally, panel E presents the results of estimating equations (1), (2), and (3) with a
control sample obtained from all firms in the CRSP/Compustat universe using
propensity-score matching (see Appendix D for details about the construction of the
control sample). Re-estimating the initial regressions with the matched pairs mitigates
potential concerns related to sample selection in the GMI data. The results mirror those
in Table 2.
The coefficients reported in Table 2 indicate that, holding everything else
constant, an increase of 5 points in the ROindex is associated with a 5% decrease in
idiosyncratic volatility, a 0.05 decrease in Beta, a decrease of roughly 10 basis points in
Allindrawn, and an increase of approximately half a notch in Rating. Although these
26
numbers are descriptive (see section 6 for a discussion of the limitations of the research
design), the results suggest that the difference in risk between firms with high and low
levels of risk oversight is economically significant.
4.2. TIME SERIES ANALYSIS BEFORE THE 2007-2008 FINANCIAL CRISIS
4.2.1. Research Design
A potential concern about the results in section 4.1 is that the association between
risk oversight and risk could be driven by unobserved firm characteristics. To mitigate
this concern, I test whether the association between risk oversight and firm risk also holds
in the time-series. Finding that firms exhibit lower risk after the implementation of risk
oversight structures mitigates endogeneity concerns because if an unobserved variable
were driving the association between risk oversight and firm risk, that variable should be
significantly correlated with risk oversight not only in the cross-section, but also in the
time-series. To test the hypothesis that there is a time-series association between risk
oversight and risk, I estimate the following equation:
DepVariablet= δ0 + δ1 RiskOversight+ δ2 DimplROt + δ3
RiskOversight*DimplROt + Controlst + εt. (4)
where DepVariablet is one of three dependent variables measured over fiscal year t:
LogIdVol, ExtremeRet and Allindrawn. DimplRO is an indicator variable that takes on
the value 1 if ROindex > 0 in year t, and 0 otherwise. RiskOversight is the value of the
firm’s ROindex at the end of the sample period (i.e., 2006). For each of the dependent
variables, Controls is a vector comprising the control variables used in equations (1)
27
through (3). If, consistent with H1, firm risk is significantly lower after the
implementation of risk oversight structures, I predict 3 is negative.
Because the time-series association between the five types of risk oversight
structures and risk might not be the same, I analyze separately each type of risk oversight
structure using the subindexes defined in section 3.2 (i.e., RCindex, ERM, RMstd, CRO
and Other). For example, for the risk committee (RCindex), I estimate a modified
version of equation (4):
DepVariablet= δ0 + δ1 DimplRCt + δ2 RiskCommittee + δ3
RiskCommittee*DimplRCt + δ 4 ERMt+ δ5 RMstdt +
δ6 CROt + δ7 Othert + Controlst + εt (5)
where DimplRC is an indicator variable that takes on the value 1 if RCIndex > 0 in year t
(i.e., if the firm has a risk committee implemented in year t), and 0 otherwise.
RiskCommittee is the value of RCindex at the end of the sample period (i.e., 2006).
RCindex, ERM, RMstd, CRO, and Other are defined in section 3.2. Finally, as robustness
check, I also estimate equations (5) and (6) using an alternative control sample obtained
through the propensity-score methodology described in appendix D.
4.2.2. Results
Table 3, Panel A, presents results of the analysis of the time-series association
between implementing a risk committee and firm risk (equation 5). The negative
interaction between RiskOversight and DimplRO (t-stats. = –3.13 and –2.98, using all
GMI data and the propensity-score matched pairs, respectively) reveals that firms exhibit
lower risk after implementing risk oversight structures. Panels B and C confirm that this
28
result holds for three proxies of risk: LogIdVol, Allindrawn, and ExtremeRet. Panel B
shows that the coefficient on the interaction term between the time indicator variable
(DimplRC) and the risk committee index (RiskCommittee) is negative and significant in
all three models. Specifically, the coefficient on the interaction term indicates that, after
implementing a risk committee, firms experience lower LogIdVol (t-stat. = –1.87), lower
ExtremeRet (t-stat. = –2.53), and lower Allindrawn (t-stat. = –3.36). Panel C shows the
results of identical specifications estimated using an alternative control sample obtained
through propensity-score matching (see appendix D about the construction of the control
sample). The results reveal the same inferences as those in Panel B.
4.3. STOCK MARKET PERFORMANCE DURING THE 2007-2008 FINANCIAL CRISIS
4.3.1. Research Design
Because from 2000 to 2006 there were years of economic growth and non-
extreme economic conditions, it is difficult to infer from the results of sections 4.1 and
4.2 whether higher risk oversight could mitigate the effects of severe systemic shocks.
To address this question, I next examine whether the negative association between risk
oversight and risk also holds during a period of abnormal economic conditions, namely
the 2007-2008 financial crisis. In particular, I test whether firms with greater levels of
risk oversight before the 2007-2008 financial crisis exhibit less sensitivity to market
fluctuations during the 2007-2008 financial crisis than firms with lower levels of risk
oversight.20
20
This analysis focuses on non-financial firms to provide further evidence that the observed association
between risk oversight and risk-related outcomes is not limited to financial institutions. For financial
institutions, this analysis gives similar results when I compare financial institutions with ROindex > 2 and
those with ROindex = 0.
29
I define the 2007-2008 financial crisis period as all trading days between August
1, 2007 and March 31, 2009.21
I estimate the Fama-French (1993) three factor model
plus momentum and interact ROindex with the excess market return:
Rirfit= δ0 + δ1 ROindexit + δ2 ROindexit *Mktrft + δ3 Mktrft +
δ 4 HMLt + δ5 SMBt + δ6 UMDt + εt (6)
where Rirfit is the firm i’s return on day t less the risk-free rate, Mktrf is the daily market
return less the risk-free rate, and HML, SMB, and UMD are the book-to-market, size and
momentum daily factors. If, consistent with H1, firms with more risk oversight are less
sensitive to stock market fluctuations, I predict that δ2 is negative; i.e., firms with more
risk oversight have lower beta. The null hypothesis is that risk oversight is not related to
systematic risk; i.e., δ2 = 0.
I next explore whether firms with higher levels of risk oversight performed better
on the worst days of the crisis than firms with lower levels of risk oversight. This
analysis can potentially be informative about whether firms with more risk oversight are
more resilient not only to stock market fluctuations in general, but also to extreme events.
In particular, I estimate equation (6) without the interaction term and using only those
days when the market return was below –1%.22
If negative and extreme stock market
events have a milder effect on firms with high levels of risk oversight, the returns of these
21
August 2007 is when the money market started experiencing serious difficulties, and March 2009 was the
last month before the 2009 partial recovery. Although the definition of the crisis period is somewhat
arbitrary, untabulated results reveal that inferences do not change for alternative definitions of the crisis
period, such as the period between January and December of 2008.
22 The results of this test are not dependent on using –1% as the market return threshold to identify days of
extremely low market returns. Specifically, I obtain similar results using days on which the stock market
return was below –1.5% and –2%.
30
firms on those event days should be higher (i.e., less negative) than the returns of firms
with low levels of risk oversight, i.e., δ1 > 0. Finally, as a robustness check, I repeat the
analysis using the propensity-score matched pairs described in appendix D.
4.3.2. Results
Table 4 presents the results of estimating equation (6) during the financial crisis
period. Panel A estimates equation (6) using all trading days from August 1, 2007 to
March 31, 2009. The first two columns of each set of results in Panel A show that, as
expected, the ROindex cannot explain cross-sectional variation in returns unrelated to risk
factors (t-stat. = –0.21). However, the interaction between ROindex and Mktrf (t-stat. = –
2.49) suggests that the sensitivity to market fluctuations of firms with higher risk
oversight is lower than that of those without risk oversight. This result holds using both
all non-financial firms in the GMI data and the matched pairs of non-financial firms used
in the propensity-score matching analysis (see Appendix D about the construction of the
control sample). Untabulated results show that the negative interaction between ROindex
and Mktrf also holds when I fully interact ROindex with the four risk factors in equation
(6).
Table 4, Panel B, presents the results of estimating equation (6) without the
interaction term on days in the crisis period when the market return was lower than –1%.
The positive coefficient on ROindex (t-stat. = 3.68) shows that, on those days,
shareholders of firms with higher risk oversight experienced lower losses than those of
firms with lower risk oversight. The magnitude of the coefficient on ROindex indicates
that, on those days, a difference of 5 in ROindex is associated with a daily difference in
31
returns of approximately 18 basis points (which compounded over the 114 days when the
market return was lower than –1% translates into a difference in returns of 1.92%).
Because it is not possible to predict the days on which the market would experience a
significant loss, I do not interpret the results of Panel B as mispricing. Instead, I interpret
the results as reinforcing the idea that firms with stronger risk oversight are less sensitive
to stock market fluctuations.
5. STOCK MARKET REACTION TO LEGISLATION RELATED TO RISK
OVERSIGHT
5.1. RESEARCH DESIGN
Equations (1) through (6) test whether risk oversight is associated with lower risk
(H1). However, these tests are not informative about whether the decrease in risk
associated with risk oversight is beneficial to shareholders (H2). The market’s reaction to
recent legislation related to risk oversight provides a setting to examine the relation
between risk oversight and shareholder value that is less subject to the endogeneity
critique than association studies that use a proxy for firm value (e.g., Tobin’s Q) as
dependent variable.
I test H2 by examining whether the market’s reaction to the Shareholder Bill of
Rights of 2009 and the Corporate Governance Reform Act of 2009 (see section 2 and
appendix C) is related to the existence of risk oversight structures in the firm.23
23
It is possible that the legislative events I analyze were anticipated by the market. Thus, I search in Lexis-
Nexis and Factiva for news related to these two events before the event dates. I find that on Sunday
32
Following Larcker et al. (2010), I estimate the following regression on the day of each
event:
AbReti = δ0 + δ1NoRiskOversighti + δ2Staggeredi + δ3ExcessPayi +
δ4NLargeInstiti + δ5NCoalitionsi + δ6IsChairi + θ Controlsi + εi (7)
where AbRet is the abnormal return for firm i on the day of the event.24
NoRiskOversight
is an indicator variable that takes the value one if ROindex = 0, and zero otherwise.
Given that these bills also included other corporate governance provisions (see Larcker et
al., 2010), equation (7) includes controls for firm-specific pay practices, institutional
ownership, and board structure. Specifically, Staggered is an indicator variable that takes
the value one if the firm’s bylaws and charter contain a staggered board provision, and
zero otherwise. ExcessPay is the natural logarithm of total annual pay for the CEO
measured in $ millions, less the natural logarithm of median pay in that year for all firms
in the same Fama-French industry group and size quintile.25
NLargeInstit is the number
of institutions with 1% or more ownership, and NCoalitions is the number of possible
small institutional investor coalitions that would collectively control 1% or more of
shares outstanding. To control for skewness in their distributions, NLargeInstit and
NCoalitions are transformed by adding one to the observed values and taking the natural
4/25/2009 the WSJ published an article announcing the upcoming Shareholder Bill of Rights. I repeat the
analysis including the trading day following 4/25/2009 and obtain similar inferences.
24 In equation (7), returns exclude dividends and distributions. This ensures that the results are attributable
to the identified events rather than to other events occurring at the firm.
25 Within each of the Fama-French 12 industry groups, firms are ranked into size quintiles in that year, for a
total of 60 (5x12) groups. Total annual pay is computed as the sum of salary, annual bonus, Black-Scholes
value of stock options (using parameters disclosed under FAS 123R), expected value of long-term
performance plans (as disclosed in the proxy statement), and expected value of restricted stock grants.
33
logarithm. IsChair is an indicator variable that takes the value one if the CEO (or any
other insider) is chairman of the board, and zero otherwise. Controls is a vector of
control variables comprising Size, BM, and Momentum. Size is the natural logarithm of
market value (in $ millions) measured as of the latest proxy filing prior to day t, BM is
the ratio of book value of equity to market value of equity as of the latest proxy filing
prior to day t, and Momentum is the market-adjusted return over the prior six months.
I focus my inferences on the sign and significance of the coefficient on
NoRiskOversight, δ1. If, consistent with H2, risk oversight can increase shareholder
value by shaping the firm’s risk in a way that is optimal for investors, and legislation is
able to remove the frictions that prevent some firms from having stronger risk oversight,
firms that do not have risk oversight practices should experience a positive reaction to
legislation enforcing risk oversight, i.e., δ1 > 0. Alternatively, if risk oversight structures
are merely window-dressing or if there are no frictions preventing those firms from
establishing risk-related governance mechanisms, the stock price reaction to legislation
enforcing risk oversight should be unrelated to the existence of risk oversight structures
in the firm, i.e., δ1 = 0.
Even in the absence of legislative actions, the risk oversight variables could be
related to daily returns because the risk oversight variables capture omitted risk or
another omitted determinants of the cross-section of returns that is correlated with risk
oversight. To address this concern, I estimate equation (7) for each trading day over the
two quarters in which the legislative actions took place, i.e., from April 2009 through
September 2009. This yields coefficients for 121 days, 119 non-event days, and 2 event
34
days. 26
I then test whether the coefficients on event days are different from the
coefficients on non-event days. This test amounts to a difference-in-difference estimator.
That is, I assess whether abnormal returns on a given day vary cross-sectionally with risk
oversight variables, and then assess whether this variation is different for event and non-
event days. Thus, I control for any temporally constant relation between abnormal
returns and the variables of interest.27
Because the Shareholder Bill of Rights Act of 2009 and Corporate Governance
Reform Act of 2009 explicitly focus on specific risk oversight structures, such as risk
committee or chief risk officer, I estimate a modified version of equation (7) substituting
the variable NoRiskOversight for variables related to the five types of risk oversight
structures. In particular, NoRiskCommittee, NoCRO, NoERM, NoRMstd, and NoOther are
indicator variables that take the value one if the firm does not have a risk committee, does
not have a CRO, does not have ERM disclosures, does not follow a risk management
standard, and does not have any committee assigned with risk oversight, and zero
otherwise.
26
I exclude days on which other regulatory or legislative actions related to corporate governance took
place. Specifically, I exclude events related to regulatory action by the SEC in regards to amendments to
Rule14a-11 (4/6/2009, 5/20/2009, 6/10/2009), the Delaware Law Amendment on Voluntary Proxy Access
(4/8/2009) and the Shareholder Empowerment Act of 2009 into the U.S. House of Representatives on
6/12/2009 by Congressman Peters. Although these regulatory and legislative actions did not include any
risk oversight provision, they did include other proposed corporate governance provisions. Classifying
those days as non-event days could lead to biased results. In any case, including or excluding those days
does not alter the inferences.
27 Other events related to macro-economic news may have occurred simultaneously with the two regulatory
events, confounding the inferences. Although this might explain significant abnormal returns on any one
day, in order to explain the cross-sectional results, it also must be the case that the response to the macro-
economic news varies with the risk oversight variables I examine. Searching in the “Business & Finance”
section of the Wall Street Journal (WSJ) I do not find any macro-economic news on those days that could
induce cross-sectional variation in a similar way as the risk oversight variables.
35
I conduct the analyses using two control samples. First, I use as control firms all
the companies in the GMI dataset. Second, I use a propensity-score-matched control
sample selected using the methodology described in appendix D. In this case, however,
the treatment sample is formed by the 504 firms with risk oversight structures that have
CRSP/Compustat and complete governance data in 2008.28
For those firms, I identify the
504 firms in the CRSP/Compustat universe that are most similar in terms of the values of
the control variables.
5.2. RESULTS
Table 5, Panels A and B, presents the results from estimating equation (7) for
each of the event days and pooling across the two events.29
Panel A shows the results for
all the firms in the GMI dataset, and Panel B shows the results using the 504 firms with
ROindex > 0 in 2008 and their 504 matched pairs. Panels A and B indicate that the
market reaction is positively related to the absence of risk oversight structures. In Panel
A, the coefficient on NoRiskOversight is positive and significant on event #2, and pooling
across the two events (t-stats. of 2.45 and 2.62, respectively). In Panel B, the coefficient
on NoRiskOversight is positive and significant on event #1, event #2, and pooling across
the two events (t-stats. of 3.48 and 2.26, and 4.11, respectively).
Panels A and B also show that the positive market reaction is concentrated in
firms that do not have a risk committee. In Panel A, the t-stats. of the coefficients on
28
Out of the 523 firms with risk oversight structures in 2008 tabulated in table 1 (panels A and B), 19 have
missing Equilar data for at least one of the variables used in the analysis. To ensure that this sample
attrition does not affect the results, I repeat the analysis without controlling for governance variables
(which relaxes the requirement of having non-missing Equilar data). The inferences for the risk oversight
variables do not change.
29 A few firms in the sample were delisted from April to July of 2009, resulting in a small difference in the
number of observations in the cross-sectional regressions on the event days.
36
NoRiskCommittee are 1.88, 3.01 and 3.42 on event #1, event #2, and across the two
events, respectively. In Panel B, the t-stats. of the coefficients on NoRiskCommittee are
1.60, 3.05, and 3.25 on event #1, event #2, and across the two events, respectively. These
results are consistent with the risk committee being a central part of the proposed
legislation (see appendix C). However, the positive market reaction is not restricted to
firms without a risk committee. Panels A and B also show that the coefficients of
NoERM are positive and significant across the two events (t-stats. of 2.28 and 2.25 in
Panels A and B, respectively). In Panel C, the coefficients on NoCRO are also positive
and significant on event #1 and across the two events (t-stats. of 2.18 and 2.22,
respectively), which is also consistent with the proposal in the Corporate Governance
Reform Act of 2009 to require American public companies to have a CRO.
The last four columns of Panels A and B show that the positive coefficients on
NoRiskCommittee for the event days are significantly different from the coefficients on
the same variable on non-event days, which are not statistically different from zero. The
mean difference in the coefficients on NoRiskCommittee between firms with and without
a risk committee on these legislative event days is 1.33% in Panel A and 1.24% in Panel
B. Panels A and B also show that the coefficients on NoRiskOversight are greater on
event days than on non-event days. In Panel A, the mean and median differences in the
NoRiskOversight coefficients are, respectively 0.35 (t-stat. = 1.51), and 0.32 (t-stat. =
1.81). In Panel B, the mean and median difference in the NoRiskOversight coefficients
is, respectively 0.58 (t-stat. = 2.01), and 0.58 (t-stat. = 2.00). Finally, the median
coefficient on NoERM also appears to be significantly larger on event days (t-stats. of
37
1.77 and 1.79 in Panels A and B, respectively). These results relating to the time series
of the coefficients suggest that the variation in returns on event days is unique to such
days, and therefore is likely to be driven by the effects of the proposed legislation, rather
than test misspecification or some omitted determinant of returns.
Overall, the documented differences in returns related to proposed corporate
governance legislation are inconsistent with the window-dressing view of risk oversight.
However, I do not interpret these results as evidence that the market believes that all
firms should have a risk committee. First, the positive coefficient on NoERM implies that
conditional on not having a risk committee, firms with ERM programs experience a
smaller positive market reaction than those with no ERM programs, which implies that
ERM programs can be substitutes for a risk committee. Thus, the results in Table 5
suggest that the market believes that, on average, it would be value-increasing for firms
to have some form of risk oversight tailored to their specific characteristics, not that all
companies should have a risk committee. Second, the positive market reaction for firms
without a risk committee documented in Table 5 is an average result, i.e., it does not
imply that the reaction was positive for all firms.
The explanation for the documented positive market reaction to risk oversight
legislation does not necessarily rely on behavioral arguments. While it is possible that, as
survey evidence suggests (e.g., The Corporate Board, 2006), some companies
suboptimally did not implement risk oversight structures over the last decade because
they did not perceive it as value-increasing, it is also possible that legislative actions were
38
expected to remove economic frictions (e.g., agency conflicts) that prevented
shareholders from instituting their desired level of risk oversight.
6. SENSITIVITY ANALYSES
6.1. ADDITIONAL CONTROL VARIABLES
To further test the robustness of the results, I include variables that could have a
confounding effect on the regression results. In particular, the literature finds that
financial transparency, board structure, insider ownership, and anti-takeover provisions
are associated with firm’s credit and equity risk (Ashbaugh et al., 2006; Ashbaugh et al.,
2009). Untabulated results reveal that the inferences do not change when the variables
used in the literature as proxies for these other governance mechanisms are included in
equation (1).30
Also, it is possible that the risk oversight index captures only the effect of the use
of derivatives and insurance contracts on firm return volatility. If risk oversight goes
beyond derivatives and insurance contracting, we should observe that ROindex has
explanatory power incremental to derivatives and insurance contracts. To test whether
this is the case, I hand-collect from SEC filings the notional amount of derivatives used
for hedging purposes. I collect these data for the treatment and control samples used in
the propensity-score matching tests for firms with ROindex > 2 and their pairs. Next, I
re-estimate equation (1), including an additional variable, Derivatives, constructed as the
30
In particular, I include in equations (1) through (3) the percentage of independent directors, the
percentage of shares owned by the CEO, an indicator variable that takes the value of 1 if the chairman of
the board is an outsider and 0 otherwise, and the governance index in Gompers et al. (2003). I also include
in the regressions proxies for financial transparency widely used in the accounting literature such as
timeliness, conservatism, relevance, smoothness, predictability and accruals quality (Francis et al., 2004).
39
outstanding notional value of the firm’s derivatives scaled by total assets. Untabulated
results reveal that the coefficient on ROindex is negative and significantly different from
zero, which indicates that the use of derivatives cannot explain the negative association
between risk oversight and risk.
I also explore the possibility that the lower risk I observe in the firms with
stronger risk oversight might be attributable to more conservative investment practices
(i.e., less risk-taking). First, I estimate a regression of research and development
expenses scaled by total assets (R&D) on ROindex and the control variables included in
equation (1). The coefficient on ROindex in this regression is positive and not
significantly different from zero, implying that, if anything, risk oversight is associated
with more risky investment activity. To test whether the negative relation between
ROindex and risk is driven by lower investment, I also include R&D as independent
variable in equation (1). The inferences do not change. Overall, these results are
inconsistent with the notion that risk oversight leads to lower levels of risk by adopting
restrictive investment policies.
6.2. ALTERNATIVE MEASUREMENT OF KEY VARIABLES
Absent a theory to justify other types of aggregation, I construct the risk oversight
index by linear and equally-weighted aggregation of the variables in the GMI dataset.
However, the literature provides several caveats on the use of this type of index (Bhagat
et al., 2008; Daines et al., 2010). For example, assuming that a board-level risk
committee will have the same effect on the firm’s volatility as the CRO might not be
always realistic. Also, the compounded effect of those provisions on the firm’s volatility
40
need not be linear. However, if it is difficult to justify ex ante the relative importance of
those provisions, it would be even more difficult to quantify their relative weights or to
justify a specific non-linearity in the aggregation. To confirm that the results do not
depend on the way risk oversight data are aggregated, I estimate equations (1) through (3)
using the weights of the first principal component of the 25 data items in the GMI
dataset. The coefficient on this alternative proxy for risk oversight is negative and
significant. I also construct alternative measures of risk oversight by simply counting the
number of risk oversight structures adopted by the firm (and thus ignoring the specific
characteristics of those structures) and by equally weighting the subindexes related to the
five types of risk oversight structures (see section 3.2). The inferences do not change.
6.3. ENDOGENEITY AND MODEL MISSPECIFICATION
As pointed out in section 4.2, one potential concern with respect to the analysis of
the association between risk oversight and firm risk is that firms self-select into risk
oversight practices. Although the results in section 4.2 suggest that it is not likely that
my inferences linking risk oversight and risk are confounded by omitted variables,
endogeneity is still a potential concern. Also, violations of the linearity assumptions in
equations (1) through (3) could lead to model misspecification and biased coefficient
estimates. Following Armstrong et al. (2010), I use propensity score matching to directly
deal with model misspecification, and bounding techniques to provide some insight into
“hidden bias”, namely the omission of unobservable variables (e.g., Rosenbaum, 2002).
41
6.3.1. Obtaining Matched Pairs
As explained by Rosenbaum and Rubin (1983) and Armstrong et al. (2010), the
propensity-score method forms matched pairs of firms with similar characteristics, but
different levels of the treatment variable, in this case risk oversight. To obtain a matched
sample of companies, I focus on the period prior to the financial crisis (2000-2006). I
take the 383 firms with risk oversight structures implemented as of 2006 (i.e., with
ROindex > 0 in 2006) and, using Derigs’ (1988) algorithm, I find the 383 companies in
the Compustat-CRSP universe that are most similar in terms of the average values of the
covariates over the 2000-2006 period.31,32
I match financial firms (SIC codes 6000-6999)
with financial firms and non-financial firms with non-financial firms. The matching
algorithm produces 211 control firms with GMI data and 172 firms without GMI data. I
next hand-collect risk oversight data for the 172 control companies not covered by the
GMI data.33
The propensity score is obtained using a logit model.
Table 6, Panel A, presents the balance of covariates after applying the matching
algorithm based on propensity score. Among the covariates that have a significant
31
I use the Compustat-CRSP universe to obtain the control group for two reasons. First, in untabulated
results I find that using only firms with GMI data it is not possible to find a control group in which the
mean and median values of the covariates are not significantly different from the mean and median values
of the covariates in the treatment group. Second, comparing the treatment firms with their best matches in
the Compustat-CRSP universe mitigates potential sample selection concerns about the regression analysis.
32 The matched sample was constructed using a nonbipartite matching algorithm suggested by Derigs
(1988), which is an optimal algorithm in the sense that it considers the potential distances between other
pairs when forming a particular matched pair. The distance between each pair is estimated as the square of
the difference between the propensity scores of both observations divided by the square of the difference in
the values of the treatment variable. 33
I do not match on a year-by-year basis for two reasons. First, to use the same treatment and control
sample for the time-series analysis described in the next subsection, the control firm for each treatment firm
should be the same each year. Second, matching on a year-by-year basis would yield substantially more
than 383 control firms, which complicates comparability and hand-collection.
42
association with risk oversight or equity and credit risk, only ROA exhibits a small
imbalance of 1%.34
6.3.2. Differences in Risk Between Matched Pairs
Table 6, Panel B, presents results from comparing measures of risk between
matched pairs. The analysis is done by partitioning by the value of ROindex in the
treatment group (ROindexT). The measures of risk that appear in the table reflect average
values of firm-year observations when the ROindexT was greater than 0, 1, 2, or 3. For
example, the values in the second set of rows of the table indicate that the average values
of Idvol for pairs where ROindexT > 1 was, respectively, 0.27 and 0.29. The results in
Panel B reveal that the levels of risk for the control firms are significantly different from
those of their peers. Panel B also shows that this difference is bigger when ROindexT
increases. For example, the difference in Beta when ROindexT > 0 is not significant (p-
value = 0.355). However, when ROindexT > 2, that difference becomes 0.14 (p-value =
0.018). Average and median values of the risk measures decrease significantly in the
treatment group as ROindexT increases. In contrast, risk measures in the control group
experience only a slight decrease (if at all) as ROindexT increases.
6.3.3. Sensitivity to Hidden Bias
To assess the extent to which the negative association between risk oversight and
risk could be driven by unobserved determinants of both risk oversight and firm risk, I
estimate the sensitivity of the results to “hidden bias,” namely correlated omitted
variables that are not balanced across the treatment and control groups. Following
34
The results in Table 2, Panel E, show that residual variation in the covariates such as this small
imbalance in ROA cannot explain the difference in risk between the treatment and control groups.
43
Rosenbaum (2002) and Armstrong et al. (2010), I estimate the magnitude of the
correlated omitted variable bias that is necessary to cause any statistically significant
differences between matched pairs to become insignificant. The parameter Γ tabulated in
Table 6, Panel B, is a measure of the sensitivity of the results to hidden bias.35
To
facilitate the interpretation of the parameter Γ, I estimate the change in the odds ratio
induced by excluding Size from the covariates. Because Size is the covariate that has the
strongest correlation and the most explanatory power in a regression of the adoption of
risk oversight structures, assessing the effect of omitting Size when forming the matched
pairs is a useful benchmark for interpreting the values of Γ obtained in the analysis. I
find that omitting Size from the matching algorithm shifts the probability of being
assigned to the treatment group from 50% to 54%, which corresponds to Γ = 1.17.36
Thus, obtaining Γ > 1.17 means that if the observed associations between risk and risk
oversight are attributable to hidden bias, the confounding variable should have an effect
on the probability of adopting risk oversight structures even bigger than that of Size. I
repeat the analysis using other control variables found to be correlated with both risk and
risk oversight: ROA, IndustryVol and PctInstit. The odds ratio (Γ) induced by these
35
As explained by Rosenbaum (2002), hidden bias exists if two firms (denoted i and j) have the same
observed covariates, but different probabilities (denoted π) of adopting risk oversight structures. The odds
that each firm adopts risk oversight structures are denoted πi/(1-πi) and πj/(1-πj) respectively. If the odds
ratio, denoted by Г, does not equal one, then the two firms have an unequal probability of adopting risk
oversight structures and hidden bias exists. Rosenbaum (2002) shows that relaxing the assumption that
Г=1 allows for a computation of the amount of hidden bias (or, the strength of a correlated omitted
variable) that is needed to alter any significant inferences. Smaller values of Г indicate statistically
significant results that are more sensitive to hidden bias. For example, a value of 2.0 in the parameter Γ
means that the results remain statistically significant if a correlated omitted variable shifts the probability of
a firm being assigned to the treatment group from 50% to 66%.
36 To obtain these numbers, I first run the propensity-score algorithm excluding Size as covariate. Then,
using the resulting matched pairs, I estimate a logit regression of being in the treatment/control group on
Size, and compute the average predicted probabilities for the treatment and control groups.
44
variables is lower than that of Size. Although this analysis does not eliminate
endogeneity concerns (it is not possible to control for all the potentially confounding
unobservable variables), it indicates that the results exhibit low sensitivity to self-
selection bias.
7. CONCLUSION
This study examines the role of organizational structures related to risk oversight.
First, I test whether there is an empirical association between the intensity of risk
oversight and corporate risk. Second, I investigate the value implications of risk
oversight.
With regard to equity risk, the evidence suggests that risk oversight is negatively
associated with idiosyncratic equity volatility and beta. With regard to credit risk, the
evidence indicates that risk oversight is positively associated with credit ratings and
negatively associated with spreads of private loans. I also document that the negative
association between risk oversight and risk holds not only in the cross-section, but also in
the time-series. That is, firms exhibit significantly lower volatility after implementing
risk oversight structures.
The 2007-2008 financial crisis introduces an opportunity to explore whether firms
with different levels of risk oversight respond differently to extreme systemic shocks.
Analyzing the sample firms’ stock market performance during the 2007-2008 financial
crisis, I find that stocks of firms with more risk oversight experienced less sensitivity to
45
market return fluctuations and that the shareholders of firms with higher risk oversight
suffered smaller losses on the worst days of the financial crisis.
Finally, I explore the value implications of risk oversight by examining the
market reaction to corporate governance legislation related to risk oversight. Controlling
for the content of the proposed legislation that is unrelated to risk oversight, I find a
significantly more positive reaction for firms that do not have observable risk oversight
structures. This result suggests that risk oversight can be beneficial for shareholders.
Overall, the results suggest that risk oversight structures are not window-dressing
mechanisms to avoid regulatory or public pressure. Instead, the evidence indicates that
firms with risk oversight structures exhibit lower risk, and that risk oversight can increase
shareholder value. However, because the need for risk oversight can vary significantly in
the cross-section, the results do not necessarily suggest that all firms should adopt a
specific form of risk oversight.
46
CHAPTER 2: MEASURING RISK-TAKING INCENTIVES
1. INTRODUCTION
The majority of monetary incentives of executives of publicly traded corporations
in the U.S. come from the change in the value of their stock and option holdings (e.g.,
Hall and Liebman, 1998; Core, Guay, and Verrecchia, 2003; Core, Guay, and Larcker,
2003). Accordingly, most empirical studies measure managerial risk-taking incentives
using equity portfolio vega (Vega), which is calculated as the change in the Black-
Scholes dollar value of an executive’s equity portfolio for a 0.01 change in stock return
volatility. This measure of risk-taking incentives has been widely used to assess whether
stock options motivate executives to undertake risky investments (Guay, 1999; Coles,
Daniel, and Naveen, 2006; Rajgopal and Shevlin, 2002), increase firm risk (Guay, 1999;
Lewellen, 2006; Low, 2009), and engage in risk substitution (Armstrong and Vashishtha,
2011).
Despite the widespread use of equity portfolio Vega, there is considerable debate
in the accounting and corporate finance literatures about how to properly measure
managerial incentives in general and managerial risk-taking incentives in particular (e.g.,
Core, Guay, and Larcker, 2003).37
There are at least three substantive concerns with Vega
as a measure of managerial risk-taking incentives. First, since Vega is measured as a
dollar change in portfolio value, it implies that managers with the same dollar Vega
37
This is similar in spirit to the Hall and Liebman (1998) discussion regarding whether managerial
incentives to increase stock price should be measured using the percentage of the firm owned by the
manager or expected change in the value of a manager’s equity portfolio for a given change in stock price
(i.e., the portfolio delta), which are referred to as the “fractional-holdings” and “dollar-holdings” measures
of incentives, respectively (Core, Guay, and Larcker, 2003).
47
measure have identical risk-taking incentives regardless of differences in their total
expected equity wealth and differences in their risk aversion. For example, an executive
with a portfolio Vega of $50,000 and expected equity wealth of $500,000 is implicitly
assumed to have the same risk-taking incentives as an executive with a portfolio Vega of
$50,000 but expected equity wealth of only $100,000. If wealth matters in executives’
utility functions (e.g., if absolute risk aversion is decreasing in wealth), ignoring cross-
sectional variation in executive wealth can confound any observed relation between Vega
and the outcome variable of interest. More fundamentally, since managerial risk aversion
relates to the shape of the manager’s utility function, it is important that a measure of
risk-taking incentives similarly captures the shape rather than the magnitude of the
manager’s payoff with respect to his or her risk-taking actions. However, since Vega is
based on dollars rather than returns, it conflates both the magnitude of the manager’s
holdings and the (local) shape of the contractual payoff.
Second, Vega is calculated using marginal changes in stock return volatility (i.e.,
0.01), which results in a measure that is a very “local” approximation of risk-taking
incentives. This local perspective is inconsistent with the observation that stock options
are used to induce managers to take strategic actions that produce relatively large
increases in firm value. If the derivative of the manager’s expected payoff is not constant
over the likely ranges of stock price and volatility, a local measure of incentives is
unlikely to provide a valid assessment of managerial incentives.38
38
A related concern is that an executive’s equity portfolio Vega is typically calculated for a 0.01 change in
the standard deviation of returns. Using a constant change across all executives and over time ignores both
cross-sectional and intertemporal differences in firms’ return distributions. For example, it is likely easier
for a manager of a firm with annualized return volatility of 50% to increase the standard deviation of his or
48
Finally, since Vega is the partial derivative of an executive’s equity portfolio
value with respect to volatility, it assumes that the sensitivity of an executive’s portfolio
value with respect to volatility is independent of changes in stock price.39
Because
managers’ risk-taking actions usually induce simultaneous changes in stock price and
volatility (due to the risk-return tradeoff that is at the heart of managerial risk-taking), it
is crucial that any measure of risk-taking incentives incorporates the cross-derivative of
executive’s equity portfolio value with respect to both volatility and stock price.
We develop a new measure of managerial risk-taking incentives that rectifies
these limiting features of Vega. Our measure is constructed by computing the expected
percentage change in the value of a manager’s equity portfolio for relatively large
percentage changes in stock price volatility (controlling for changes in stock price, but
taking into account the cross-partial derivative which reflects the correlation between
changes in price and volatility). We label this measure “Risk Elasticity” (RiskElasticity).
This measure has a number of advantages relative to equity portfolio Vega as a measure
of risk-taking equity incentives. First, RiskElasticity is expressed in returns so that it
measures relative (i.e., percentage) changes, as opposed to absolute (i.e., dollar) changes
in managerial wealth.40
Incorporating the preexisting level of the executive’s wealth into
her firm’s returns by 0.01 than it is for a manager of a firm with return volatility of 20% to increase the
standard deviation of his or her firm’s returns by 0.01. Equity portfolio delta is less susceptible to this
concern because it is calculated for a 1% increase in stock price. Moreover, the use of an absolute value
(i.e., 0.01) over which to calculate the change in Vega is inconsistent with the use of a percentage change
(i.e., 1%) with which to calculate delta.
39 The partial derivative of the Black-Scholes option value with respect to stock volatility is
where p is stock price and the rest of the inputs are as usually defined (see later sections
of the paper).
40 One potential concern with an incentive measure based on returns on managerial wealth is that an
executive’s firm-specific equity holdings are only part of the executive’s total executive wealth. However,
49
our incentive measure reduces the effect of unobserved cross-sectional differences in
managerial absolute risk aversion induced by different levels of wealth and removes the
large cross-sectional differences in the scale of managers’ holdings.41
Moreover, the
differential tax treatment of restricted stock and stock options compounded by cross-
sectional differences in managerial portfolio composition can induce variation between
before-tax and after-tax measures of equity portfolio value (e.g., Hanlon and Heitzman,
2010). Thus, a related benefit of a return-based measure is that it is less sensitive to cross-
sectional differences in tax positions of executives.42
Second, RiskElasticity is “global” in
the sense that it is computed using changes in stock return volatility that are much larger
than the 0.01 change in volatility that is used to calculate Vega. This more accurately
captures the shape of the manager’s contract over the relevant ranges of price and
volatility outcomes. Finally, RiskElasticity explicitly accounts for the corresponding
change in stock price that is likely to accompany a change in a firm’s risk. Thus,
previous research documents that managers’ firm-specific equity holdings are usually correlated with their
other (unobservable) wealth that is unrelated to the firm (e.g., Becker, 2006).
41 If absolute risk aversion varies with the level of wealth, a dollar change in wealth would translate into
different marginal utilities for two managers with different levels of wealth. However, under standard
theoretical assumptions, a 1% change in wealth would translate into similar (or at least less different)
marginal utilities for the two managers. This argument assumes that cross-sectional differences in relative
risk aversion do not have a significant effect on managerial actions, because those differences are likely due
to behavioral factors that cancel out on average.
42 Managerial risk-taking incentives are induced by stock options, because the value of stock holdings is not
sensitive to changes in firm volatility. The intrinsic value of stock options is included in the executive’s
income on the exercise date. If t is the executive’s income tax rate, v is the current value of the manager’s
stock option portfolio, and v is the change in v due to a unit change in firm volatility, then the return on
the manager’s portfolio for a unit change in volatility is given by
. In contrast, the dollar change
in the value of the manager’s stock option portfolio is (1-)v. Thus, although a measure of risk-taking
incentives based on portfolio returns is insensitive to tax considerations, the before-tax and after-tax values
of Vega can vary significantly due to differences in tax rates compounded by differences in the composition
of managerial equity portfolios. Because managers’ marginal income tax rates are not observable, it is
plausible that Vega could suffer from “hidden bias” from differences in managers’ marginal tax rates.
50
RiskElasticity is a more “pure” measure in the sense that it only measures managers’ risk-
taking incentives rather than some combination of managers’ incentives to increase stock
price and a manager’s incentives to increase volatility.
Given that the limitations of Vega would also seem to apply to Delta as a measure
of managerial equity incentives to increase stock price, a natural question is why we
focus on risk-taking incentives. First, risk-taking incentives are the distinguishing feature
of stock options relative to restricted stock and other common forms of incentive-
compensation. Second, risk-related agency problems are of first-order importance and
stock options are the most prevalent contractual mechanism used to mitigate these
problems. Finally, given the increased focus on managerial risk-taking incentives (due in
part to the recent financial crisis), it is important for researchers to have an accurate and
powerful measure of managers’ equity risk-taking incentives.
We find that RiskElasticity exhibits a strong statistical association with a variety
of outcome variables that are commonly used to measure executive risk-taking. For
example, we find that RiskElasticity exhibits a strong positive association with future
return volatility, future idiosyncratic and systematic risk, extreme stock price outcomes,
R&D expenditures, and a variety of debt contracting variables that are likely to reflect
managers’ risk-shifting incentives. We also find that RiskElasticity almost always results
in a higher increase in explanatory power than does Vega. Moreover, RiskElasticity
frequently subsumes the explanatory power of Vega when both are included in the same
specification. Finally, we find that our primary results are robust to a number of
51
sensitivity analyses. Collectively, our results suggest that RiskElasticity is superior to
Vega as a cross-sectional measure of managerial risk-taking incentives.
The remainder of the paper is organized into five Sections. The next Section
develops the RiskElasticity measure of managerial risk-taking incentives and describes its
functional properties. Section 3 describes the sample and variables that we use in our
empirical analysis of managerial risk-taking. Section 4 presents the results from
examining the relationship between RiskElasticity and Vega and a variety of common
risk-taking outcomes that are relevant for the firms’ shareholders (e.g., stock return
volatility) and creditors (e.g., credit ratings). Section 5 presents a series of robustness
analyses to assess the sensitivity of our results to alternative functional forms of the
relationship between managerial risk-taking incentives and these risk-taking outcomes.
And, given the nature of RiskElasticity, we also ensure that our primary results are not
sensitive to any of the particular assumptions that underlie our calculation of
RiskElasticity. Concluding remarks and suggestions for future research are provided in
Section 6.
2. EQUITY PORTFOLIO RISK ELASTICITY
In this section we describe the computation of our measure of risk-taking
incentives, namely equity portfolio risk elasticity (RiskElasticity). Conceptually, this
measure is estimated as the elasticity of the manager’s equity portfolio with respect to
stock return volatility (i.e., relative changes in portfolio value for relative changes in
stock return volatility). To estimate RiskElasticity, we relax two assumptions implicit in
52
the computation of Vega, namely that the derivative of portfolio value is constant at every
point of stock return volatility and that the derivative of portfolio value is independent of
corresponding changes in stock price that are likely to accompany a change in stock
return volatility.
Let v be the value of the manager’s equity portfolio and p0 and ζ0 be the ex ante
(i.e., beginning of the period) stock price and volatility, respectively. A manager’s equity
portfolio return (rmgr) for any pair of stock price and volatility values (p, ζ) is given by:
(1)
Our measure of risk-taking incentives, “Risk Elasticity” (RiskElasticity), is
defined as the return on a manager’s equity portfolio that is due to variation in stock
return volatility, netting out the portion of the portfolio return that is due solely to
variation in stock price (i.e., holding ζ constant at the initial value ζ0), but including the
portion of the portfolio return that is due to simultaneous variation in volatility and stock
price (i.e., the cross-partial derivative).
(2)
Figure 1 provides a graphical depiction of RiskElasticity. This figure shows that
RiskElasticity is the “volume” or accumulated return on the manager’s portfolio (rmgr)
induced by increases in stock return volatility (i.e., the volume defined by the points O-
E-C-D-A-B)adjusting for the accumulated return on the manager’s portfolio induced by
increases in stock price p, holding constant at 0 (i.e., the volume defined by the points
O-E-A-B-G-F). The latter part of the above computation is essentially the portion of the
portfolio return that is due solely to variation in stock price, which we label the “Price
53
Elasticity” (PriceElasticity). Although PriceElasticity can be interpreted as managerial
incentives to increase stock return, it is also a byproduct of measuring RiskElasticity and
therefore does not have the same properties as portfolio delta.
To estimate RiskElasticity (and PriceElasticity), we use numerical simulations to
compute the returns that would accrue to a manager’s equity portfolio for different
combinations of price and volatility, (p, ζ). Specifically, we consider relative changes in
both parameters within a range of 0 to +100%:
(3)
We vary the parameters p and ζ in 10% increments, or r {0, 0.1, 0.2, ..., 0.9, 1} and
{0, 0.1, 0.2, .., 0.9, 1}. We obtain estimates of p₀ and ζ₀ from historical data where p₀ is
the stock price as of the end of the fiscal year and ζ₀ is the annualized return volatility.
We estimate the value of manager’s equity portfolio, v, as the sum of the value of the
manager’s options according to the Black-Scholes formula as modified by Merton (1973)
and the value of the manager’s stock and restricted stock holdings valued at the price p.
It is important to note that because the support of the function rmgr varies from 0
to 1 along both axes, measures of accumulated and mean, or average, returns are
equivalent. Thus, RiskElasticity can be interpreted as the average return that the manager
would earn over all possible relative increases in volatility up to 100%. This average
return also accounts for all possible relative increases in stock price that could
54
accompany those increases in volatility without making any assumption about a potential
relation between values of stock price and volatility.43
To illustrate, consider the equity portfolio holdings and associated incentive
estimates for the Chief Executive Officers (CEOs) of Celebrate Express Inc. (Kevin A.
Green) and Aspreva Parrmaceuticals Corp. (Richard M. Glickman). On December 31,
2006, Green held an equity portfolio with a Black-Scholes value of $272,000, Vega of
$11,000, and delta of $5,000, while Glickman held an equity portfolio with a Black-
Scholes value of $25,742,000, Vega of $10,000, and delta of $261,000.44
Thus, although
Glickman had substantially more wealth invested in his firm, the two CEOs had very
similar Vegas.
However, Green would earn a return of nearly 4% on his firm-specific wealth
from a 0.01 increase in stock return volatility (holding average stock returns constant),
while Glickman would only earn a return of only about 0.03% for a similar 0.01 increase
in stock return volatility. Holding stock return volatility constant, both executives would
earn a similar return from a 1% increase in stock return (specifically, 1.8% for Green and
1.0% for Glickman). Clearly, the risk-taking incentives of the two executives are very
43
We acknowledge that not all (p,) pairs are feasible or equally likely. However, assuming a specific
relation between stock price and volatility is also likely to be problematic because we do not know the
distribution of returns and volatility anticipated by the manager. In Section 5, we show that considering a
potential risk-return tradeoff in managerial decision-making does not alter any of our reported inferences
related to RiskElasticity.
44 Mr. Green’s employment began in May 2006, when he received a grant of 300,000 out-of-the-money
options and no stock. In contrast, Glickman, who had been CEO for 5 years, held 1,215,173 shares, 41,875
unexercisable options and 28,875 exercisable options, some in-the-money, and some out-of-the money at
the end of 2006.
55
similar when measured using Vega, but very different using a measure based on
elasticity.
Despite their similar Vegas, their estimated risk elasticities are very different. In
particular, Green has a RiskElasticity of 1.282 while Glickman has a RiskElasticity of
only 0.008. In the case of Green, his RiskElasticity of 1.282 means that over the range of
possible increases in stock price and stock return volatility up to 100%, the average return
on his equity portfolio is 128%. In contrast, the average return on Glickman’s equity
portfolio over a similar range of increases in stock price and return volatility is only
0.8%. Figure 2 graphically depicts these differences between Green’s and Glickman’s
equity portfolios. This figure shows that Green’s portfolio return shows a significant
upside with respect to percentage increases in volatility, Glickman’s is fairly insensitive
to risk, despite having a significant number of stock options in his portfolio. The relative
insensitivity of Glickman’s equity portfolio return to volatility is due to Glickman’s
relatively large stock holdings, with a Black-Scholes value that is independent of firm
volatility.45
This example also illustrates the potential limitations of measuring portfolio value
sensitivities by extrapolating the values of Vega to changes in volatility greater than 0.01.
Specifically, assuming that portfolio value sensitivity to volatility is proportional to Vega,
a 0.2 increase in annual volatility (the average increase in volatility in the sample) would
45
The theoretical incentives literature (e.g., Lambert et al., 1991; Ross, 2004) shows that, ceteris paribus,
equity portfolio delta (which is provided by both stock and stock options) provides an incentive for a risk-
averse manager to reduce firm risk. Thus, the traditional measures of equity incentives (i.e., Delta and
Vega) both contain some measure of risk-taking incentives: namely Vega provides incentives to increase
risk and delta provides incentives to decrease risk. An additional benefit of RiskElasticity is that it isolates
the risk-taking incentives from stock and stock options and combines them into a single measure of risk-
taking incentives.
56
be assumed to produce an 80.88% increase in Green’s portfolio value. However, a 0.2
increase in volatility would actually result in an increase of only 40.81% in Celebrate’s
volatility (Celebrate’s annualized return volatility in 2006 is 0.49) and this would, in turn,
result in an increase of 93.85% in Green’s portfolio value (this can be seen in the bottom
right panel of Figure 2). In contrast, for Glickman, these amounts are 0.77% and 0.57%,
respectively (Aspreva’s annualized return volatility in 2006 is 0.59). Thus, assuming that
portfolio value sensitivity to stock volatility is proportional to Vega underestimates the
return that would accrue to Green and overestimates the return that would accrue to
Glickman.
Another important point is that risk elasticity cannot be computed by simply
deflating Vega by the manager’s portfolio value. The illustration above shows that
extrapolating local changes in volatility that are used to compute Vega to larger “global”
values is not appropriate because this simple approach ignores the curvature of the
manager’s return function with respect to increases in return volatility, and it is the shape
of the manager’s return function that is at the heart of his or her risk-taking incentives.
Moreover, risk elasticity is based on relative changes in volatility (i.e., a change in
volatility relative to current volatility), as opposed to absolute changes in volatility (i.e.,
0.01 or some other constant value), which makes it more suitable as a cross-sectional
measure.
Finally, this example also illustrates how risk elasticity “disentangles” the
interdependent components of the change in equity portfolio value that are attributable to
changes in volatility and changes in price. To do this, we estimate the part of the volume
57
of the manager’s return function that is induced by the cross-derivative (namely, the
derivative of the manager’s return with respect to volatility and price or
). For
Green, this value is 33.35%, whereas for Glick this value is 0.006%. Thus, ignoring the
interaction between risk-taking and return incentives can lead to underestimating
managerial risk-taking incentives and omitting important cross-sectional differences in
risk-taking incentives.
In subsequent sections we calculate various measures of equity incentives for a
large sample of executives and explore the cross-sectional empirical performance of these
measures. In particular, we evaluate the ability of these measures to explain outcomes
that reflect either actual or anticipated managerial risk-taking activites.
3. SAMPLE AND VARIABLE MEASUREMENT
We use a database provided by Equilar, Inc. to identify our sample of firms and to
construct the various measures of managerial risk-taking incentives. The Equilar
database is similar to ExecuComp in that it provides executive compensation and equity
holdings data collected from annual proxy filings (DEF 14A) with the U.S. Securities and
Exchange Commission (SEC). However, the Equilar database has much broader
coverage than ExecuComp and provides an average of 4,024 firm observations (in
contrast to the roughly 1,500 firm observations available annually from ExecuComp) in
each year during our sample period that covers the 2000 to 2008 fiscal years.46
46
Our year labeling follows Compustat’s convention where firms with fiscal years between (say) June,
2007 and May, 2008 are labeled as year 2007.
58
Each year we calculate RiskElasticity and PriceElasticity for each manager as
described in the previous section. We also following a large body or prior research
(Guay, 1999; Core and Guay, 2001; Core and Guay, 2002; Rajgopal and Shevlin, 2002;
Coles et al., 2006; Low, 2009; Armstrong and Vashishtha, 2011) and calculate Vega and
Delta as alternative measures of risk-taking and stock price incentives, respectively.47
Specifically, we calculate Vega as the change in the risk-neutral (i.e., Black-Scholes)
value of the executive’s option portfolio for a 0.01 change in the standard deviation of the
underlying stock returns.48
Similarly, we follow prior literature and measure managerial
incentives to increase stock price using equity portfolio Delta, which is calculated as the
change in the risk-neutral value of the executive’s equity portfolio for a 1% change in the
price of the underlying stock. To construct a firm-specific measure of incentives, we
average the previous incentive variables across all the executives in the company for
which there are available Equilar data. Each incentive variable is winsorized at the 1st and
99th
percentiles to ensure that our results are not due to unusual observations or
47
We use the Black-Scholes framework to estimate managerial equity portfolio value. Specifically, option
value is calculated as – – ), where – .
As is customary in the corporate finance literature (e.g., Core and Guay, 2002), we measure the inputs of
the Black-Scholes formula as follows: p is the stock price at the end of the fiscal year, and is the
annualized return volatility (estimated as the standard deviation of daily logarithmic stock returns during
the 120 trading days before the fiscal year end multiplied by the square root of 250). T is the remaining
time to maturity of the option in years, as of the fiscal year end multiplied by 0.7 to account for the
prevalence of early exercise. X is the exercise price of the option. r is the natural logarithm of one plus the
risk-free interest rate, which is the interpolated yield, as of fiscal year end date, on a U.S. Treasury strip
with the same time to maturity as the remaining life of the stock option. d is the natural logarithm of one
plus the expected dividend rate, which is measured as the dividends paid during the previous fiscal year
scaled by the year-end stock price. Also following previous literature (Guay, 1999), we ignore Vega from
stock holdings and aggregate the values of all the securities owned by the executive in the current fiscal
year (namely, stock options and stock holdings). 48
Guay (1999) shows that the Vega from shares of stock is insignificant for all but the most financially
distressed firms, where equity becomes more like an at-the-money option. Consequently, the Vega from a
CEO’s option portfolio is several orders of magnitude larger than the Vega from the CEO’s stock portfolio.
Following prior literature (e.g., Coles et al., 2006; Low, 2009), we ignore Vega from stock holdings and
measure CEO equity portfolio Vega as the Vega of the CEO’s option holdings.
59
“outliers.” A description of the remaining variables used in our analyses is provided in
the Appendix.
Panel A of Table 7 presents distributional statistics for the primary variables in
our analyses. Notable from this table is that our estimates of Vega and Delta are
somewhat smaller than those reported in previous studies such as Coles et al. (2006),
Low (2009), and Armstrong and Vashishtha (2011). This occurs because our sample
firms are drawn from Equilar rather than Execucomp and the former database has much
broader coverage and includes a larger number of smaller companies. Consistent with
prior studies (e.g., Coles et al., 2006; Low, 2009; Armstrong and Vashishtha, 2011), Vega
and Delta are both highly skewed in our sample. Specifically, Vega has median and mean
values of $8,650 and $27,400, respectively, and Delta has median and mean values of
$53,900 and $204,780, respectively. In contrast, both RiskElasticity and PriceElasticity
are relatively more symmetric and have median and mean values of 0.09 and 0.12 for
RiskElasticity and 0.63 and 0.68 for PriceElasticity, respectively. The interpretation of
RiskElasticity for our sample is the equity portfolio value of a manager in an average
(median) firm would increase by 12% (9%) on average over the selected range of
increases in volatility, adjusting for the accompanying increase in stock price. Similarly,
the PriceElasticity values in Panel A of Table 7 imply that, for our sample, the equity
portfolio value of a manager in an average (median) firm would increase by an average of
68% (63%) over the selected range of increases in stock price, if there were no increase
in stock return volatility.
60
Panel B of Table 7 presents a correlation matrix (Spearman rank-order
correlations and Pearson product-moment correlations above and below the diagonal,
respectively) between the primary variables in our analysis. A few notable features
emerge from this table. First, there is a relatively modest correlation between
RiskElasticity and equity portfolio Vega (the Spearman correlation is 0.33 and Pearson
correlation is 0.07). These two risk-taking incentives measures also exhibit very different
correlations with the equity portfolio value. Specifically, we find that Vega exhibits a
positive and significant correlation with equity portfolio value (Spearman of 0.54 and
Pearson of 0.33), which indicates that, among other things, this variable captures a
moderate amount of the cross-sectional variation in the value of executives’ equity
portfolio holdings. In contrast, RiskElasticity exhibits a significant negative relation with
equity portfolio value (Spearman of –0.28 and Pearson of –0.14). These correlations
indicate that RiskElasticity captures a different dimension of risk-taking incentives than
equity portfolio Vega, and thus is less likely to be confounded by cross-sectional
differences in the level of executives’ equity portfolios.
Panel B of Table 7 also shows that Vega exhibits a large positive correlation with
firm size (Spearman of 0.67 and Pearson of 0.61), whereas RiskElasticity exhibits only a
modest (negative) correlation with firm size (Spearman of –0.12 and Pearson of –0.13).
These results suggest that RiskElasticity is less sensitive to scale effects than Vega. Scale
independence is a desirable property because scale effects can make it difficult to
econometrically distinguish, or identify, the effect of incentives from the effect of firm
size or the effect of the level of managerial equity wealth. Finally, Panel B of Table 7
61
also reveals that Delta and portfolio value (VPortf) are extremely highly correlated (0.99
for both the Spearman and Pearson correlations). This makes it difficult to empirically
identify whether Delta captures the sensitivity of the manager’s portfolio to changes in
stock price, or whether it simply captures the scale or magnitude of managers’ equity
holdings (Armstrong, 2010).
4. EMPIRICAL ANALYSIS OF RISK ELASTICITY
In this section, we examine empirically whether RiskElasticity is more descriptive
of risk-taking behavior than Vega. In particular, we test the statistical relation between
these two measures and various outcomes that reflect either actual or anticipated
managerial risk-taking activites that are relevant for firms’ equity holders and creditors.
Since many of the underlying parameters that are necessary for precisely measuring
managerial incentives are unobservable (e.g., the class of utility function, risk aversion,
and the amount and composition of wealth), the efficacy of any measure of managerial
risk-taking incentives is ultimately an empirical question. Therefore, we gauge the
performance of RiskElasticity on this basis by examining its ability to explain a host of
outcomes that reflect different dimensions and types of realized and anticipated
managerial risk-taking activities.
4.1. RISK-TAKING INCENTIVES AND EQUITY RISK
Risk-averse and undiversified managers who have most of their wealth tied to the
value of their firm can have an incentive to reject positive net present value projects that
also increase firm risk. One potential solution to this agency problem is to introduce
62
convexity (e.g., stock options) into the manager’s compensation contract to counteract the
effects of the manager’s risk aversion and make his or her interests more in line with
those of the firm’s shareholders (e.g., Haugen and Senbet, 1981; Smith and Stulz, 1985).
A considerable body of theoretical (Lambert et al., 1991; Carpenter, 2000; Ross, 2004)
and empirical research (Guay, 1999; Rajgopal and Shevlin, 2002; Hanlon et al., 2004;
Coles et al., 2006; Low, 2009) has investigated the relation between stock options and
managers’ risk-taking behavior. If there are cross-sectional differences in managers’ risk-
taking equity incentives, then these should be reflected in cross-sectional differences in
realized equity risk.
4.1.1. Future Stock Return Volatility
Our first set of results presented in Panel A of Table 8 follows a large body of
prior research (e.g., Guay, 1999; Hanlon et al., 2004; Coles et al., 2006; Low, 2009;
Brockman et al., 2010) and measures firms’ equity risk using one-year-ahead future
realized return volatility. The first column presents the results using only firm
characteristics as control variables (i.e., Size, BM, Leverage, and ROA). The results are
generally consistent with prior research (e.g., Guay, 1999; Rajgopal and Shevlin, 2002;
Hanlon et al., 2004; Low, 2009) and show that volatility is decreasing in firm size and
operating performance and increasing in leverage. The second column includes
managerial risk-taking incentives, measured as RiskElasticity. We also include
PriceElasticity to control for managerial incentives to increase stock price, and the value
of the executive’s portfolio (VPortf) to capture cross-sectional differences in the scale of
63
executives’ equity portfolios.49
Finally, we also include two controls, CashComp and
Age, which have been used in prior research (e.g., Gibbons and Murphy, 1992; Guay,
1999; Gao, 2010) as controls for managerial risk preferences.50
We find that RiskElasticity exhibits a strong positive relation with future stock
return volatility (coefficient of 0.685 and t-stat of 4.49), which is consistent with
RiskElasticity capturing ex ante managerial risk-taking incentives that are manifest in the
form of future volatility. We also find that PriceElasticity exhibits a strong negative
relation with future volatility (t-stat of –7.01), which is consistent with some previous
research that finds that, ceteris paribus, managers with greater incentives to increase
stock price (e.g., Delta) tend to dislike risk (e.g., Knopf, Nam, and Thornton, 2002; Coles
et al., 2006).51
The incremental unadjusted R2 for RiskElasticity and PriceElasticity
49
The correlation matrix in Panel B of Table 1 shows that, unlike Delta and Vega, RiskElasticity and
PriceElasticity are relatively uncorrelated with the size of executives’ equity portfolios. Therefore, a
potential concern is that two executives who only hold shares of stock (i.e., neither has any options) will
have exactly the same PriceElasticity, regardless of any difference in the number of shares held. In other
words, both managers will earn a 1% return on their equity portfolio for every 1% stock return. We
therefore control for portfolio value in the regression to capture differences in the scale of their equity
holdings. (Edmans et al., 2009 make a similar point in their footnote 12.) However, when we include both
RiskElasticity and Vega (and PriceElasticityand Delta) in the same specification, we do not include VPortf
due to its very high correlation with Delta (Pearson and Spearman correlations of 0.99). 50
It is possible that the compensation contracts of newly hired executives provide more risk-taking
incentives than those of executives with longer tenure. Although we do not have a clear prediction for the
effect of executive tenure on risk-taking incentives, when we include CEO tenure in our regressions, we
find that our inferences do not change.
51 The empirical evidence on the association between Delta and risk-taking is somewhat mixed. For
example, Coles et al. (2006) report that Delta is positively associated with firm return volatility, which
suggests that Delta encourages risk taking, but that Delta also makes managers more risk averse by
encouraging them to increase capital expenditures, decrease R&D expenditures, and decrease leverage.
Low (2009) also concludes that her evidence on the relationship between Delta and managerial risk taking
is inconclusive. The theoretical literature (Ross, 2004), suggests that this ambiguous relationship between
Delta and firm risk could be caused by two compounding effects. On the one hand, since Delta magnifies
the concavity of a manager’s utility function, it gives them an incentive to reduce risk. On the other hand,
assuming that risk aversion decreases with the level of wealth, additional stock grants could bring
compensation into a range where risk aversion is less and thus induce risk taking. Following these
theoretical arguments, our interpretation of the negative association between PriceElasticity and volatility
64
relative to the control variables is 6.91% and the associated F-stat. is 672.19 (p-value <
0.001). The third column uses Vega and Delta as measures of risk-taking incentives and
incentives to increase stock price, respectively. We find that both Vega and Delta have a
positive and significant association with future return volatility (t-stats of 1.86 and 3.23,
respectively). The incremental explanatory power for Vega and Delta is 0.78% and the
associated F-stat is 87.99 (p-value < 0.001), which is substantially smaller than those for
RiskElasticity and PriceElasticity. To compare the explanatory powers of the models in
the second and third column of Table 8, Panel A (i.e., using RiskElasticity versus using
Vega) we estimate a Vuong test to test which of the two non-nested models is closer to
the “true” model. The Z-statistic in Vuong test is 6.12, which suggests that it is safe to
reject the hypothesis that the models are equally close to the true model.
Given that RiskElasticity and Vega both exhibit the predicted significant positive
relation with future realized volatility, we include these measures together (along with
PriceElasticity and Delta) in the fourth column. We find both measures of managerial
risk-taking incentives are positive and significant, which suggests that RiskElasticity
explains dimensions of firm risk that are not captured by Vega. Since volatility is known
to be persistent, we include lagged volatility to control for the level of volatility to focus
on innovations in volatility. Thus, by controlling for lagged volatility, our final
specification relies more on time-series rather than cross-sectional variation in the
dependent variable.
is that, because it is measured in returns (thus reducing the effect of wealth on risk aversion),
PriceElasticity potentially mitigates the second effect and captures mainly the first effect.
65
As expected, we find that lagged volatility is positive and highly significant,
which indicates that volatility is persistent. And, although the statistical significance of
the coefficient is somewhat diminished, we find that RiskElasticity remains significantly
associated with future volatility (t-stat of 2.17). In contrast, the coefficient on Vega
becomes statistically indistinguishable from zero in this specification, suggesting that
RiskElasticity, but not Vega, explains the association between risk-taking incentives and
return volatility in the time series.
4.1.2. Future Idiosyncratic and Systematic Risk
As theoretical (Duan and Wei, 2005; Henderson, 2005; Acharya and Bisin, 2009)
and empirical (Armstrong and Vashishtha, 2011) research suggests managers’ equity
holdings provide them with differential incentives to take idiosyncratic and systematic
risk. We therefore examine the relation between risk-taking incentives and the separate
components of total risk. Table 8, Panel B presents results that parallel those in Panel A,
but using future idiosyncratic return volatility as the measure of firm risk. The results are
similar to those when total volatility is the dependent variable: namely a positive and
significant relation between both RiskElasticity and Vega and future idiosyncratic risk
separately (in the second and third columns) and when they are both included together in
the specification (in the fourth column). Since idiosyncratic risk is also highly persistent,
we include lagged idiosyncratic volatility in the final column and again find that the
coefficient on RiskElasticity remains positive and significant, while that on Vega
becomes insignificant.
66
In Table 8, Panel C, we again estimate a similar specification using future
systematic risk (measured as Beta) as the measure of firm risk. We estimate Beta as the
coefficient in a regression of daily excess returns on the CRSP value-weighted excess
market return over the 250 days prior to the fiscal year end. In the second column, we
find that RiskElasticity exhibits a strong positive relation with future systematic risk.
However, in the third column, we find a strong negative relationship between Vega and
future systematic risk. This finding is inconsistent with recent theoretical arguments and
empirical evidence that suggests risk-taking equity incentives are strongest for systematic
risk because this type of risk can be hedged. When both RiskElasticity and Vega are
included together in the specification, we continue to find that RiskElasticity is positively
and significantly associated with future systematic risk and Vega is negatively and
significantly associated with future systematic risk. Finally, in the last column, we find
that these relations continue to hold in the presence of lagged systematic risk.
Collectively, the evidence in Table 8 suggests that, at best, Vega is a weak measure of
risk-taking equity incentives. And the results in Panel C in particular cast doubt on the
efficacy of Vega as a proxy for managerial risk-taking incentives given that equity-based
risk-taking incentives are strongest for systematic risk.
4.2. RISK-TAKING INCENTIVES AND CREDIT RISK
Fama and Miller (1972) and Jensen and Meckling (1976) show how shareholders
have incentives to engage in “risk shifting” or “asset substitution” whereby they invest in
risky investments and shift wealth away from bondholders. A number of theoretical
studies (e.g., Brander and Poitevin, 1992; John and John, 1993) argue that when
67
designing compensation contracts and their associated risk-taking incentives, boards
consider that the firm’s other stakeholders (primarily its creditors) will also anticipate
these risk-taking and risk-shifting actions and will price protect their contracts
accordingly.52
To measure credit risk, we first use the firm’s average credit rating for the next
fiscal year t (Ratingt+1). Rating ranges from 1 to 21, with 1 indicating the lowest rating
and 21 indicating the highest rating. Because Rating is an ordinal variable, we estimate
the ratings regressions using ordered logit. We also follow prior literature and use the
same specification as in the previous tests except for the following two changes. First, we
add Volatility distinguish the effect of risk-taking incentives on credit risk from equity
risk. Second, we include the natural logarithm of total assets (logTA) rather than the
market value of equity as a proxy for size, because the value of total assets is more
relevant to creditors than the market value of the firm’s equity. The results in the first
column of Table 9, Panel A, are broadly consistent with prior studies (e.g., Ashbaugh,
Collins, and LaFond, 2006) and we find that credit ratings are increasing in firm size
(measured as total assets) and operating performance and decreasing in leverage and
return volatility. In the second column, we find a negative and significant relation
between RiskElasticity and credit ratings, which suggests that creditors anticipate risk-
taking incentives from RiskElasticity. In the third column, we find that Vega exhibits a
positive and significant relation with credit ratings, which is inconsistent with the notion
52
Brockman et al. (2010, p. 1124) cite a 2007 Moody’s Investors Service Special Comment that describes
how “Executive pay is incorporated into Moody’s credit analysis of rated issuers because compensation is a
determinant of management behavior that affects indirectly credit quality (p. 1).”
68
that Vega provides managers with risk-taking incentives. In the last column when both
RiskElasticity and Vega are included the specification, we continue to find a positive and
significant coefficient on RiskElasticity and a negative and significant coefficient on
Vega.
Because credit ratings are subject to measurement error and are expected to be
affected by the incentives of credit rating agencies, we also follow prior literature (e.g.,
Bharath et al., 2009) and use the “all in drawn spread” (Allindrawnt+1) of private loans
contracted by the company during the next fiscal year (as reported by Dealscan) as an
alternative measure of credit risk. To estimate the association between risk-taking
incentives and all-in-drawn spreads we use the control variables in the credit rating model
and three additional control variables related to private loans: Dealamount, the loan
amount (in millions of dollars), Maturity, the duration of the loan (in months), and
Secured, an indicator that takes a value of one if loan facility/bond is secured with
collateral and zero otherwise. The results in the first column of Table 9, Panel B are
generally consistent with prior studies (e.g., Bharath et al., 2009) and show that firms’
cost of borrowing is decreasing in firm size, prior operating performance, and maturity,
and increasing in leverage, prior stock returns, and when it is secured. In the second
column, we find that RiskElasticity exhibits a strong positive relation (t-stat of 6.50) with
Allindrawnt+1. This is consistent with RiskElasticity capturing managerial risk-taking and
risk-shifting incentives and the firms’ creditors price protecting against this in the form of
a higher spread. In the third column, we find that Vega exhibits a significant negative
relation with Allindrawnt+1. This is again inconsistent with the notion that Vega captures
69
risk-taking and risk-shifting incentives. Collectively, the results in Table 9 are consistent
with RiskElasticity, but not Vega, capturing risk-shifting incentives and creditors
anticipating and price-protecting against these actions.
4.3. RISK-TAKING INCENTIVES AND ALTERNATIVE MEASURES OF RISK-TAKING
BEHAVIOR
Previous studies generally take one of two alternative approaches to measuring
managers’ risk-taking decisions. The first group of studies (e.g., Guay, 1999; Coles et al.,
2006; Low, 2009) use realized return volatility as a proxy for managerial risk-taking. The
advantage of this measure is that it is comprehensive and should capture the effects of all
the risk-taking decisions the manager makes. The limitation of using future return
volatility is that it captures not only the outcome of managerial risk-taking decisions, but
also a firm’s disclosures, information trade in the firm’s shares, informational demands of
the firm’s investors, and other features of the firm’s information environment (e.g., Roll,
1988; Ross, 1989).53
Accordingly, in this section, we repeat the previous tests using three
alternative measures of risk-taking behavior: extreme stock returns, implied volatility and
R&D investment.
4.3.1. Extreme Stock Returns
Our next set of tests borrows from Sanders and Hambrick (2007) and uses
relatively extreme stock returns as the outcome variable. For this analysis, we construct
an indicator (Extreme) that takes a value of one if the firm’s compound return over the
53
Another concern with future realized return volatility when using Vega as the measure of risk-taking
incentives is that Vega is a function of current stock return volatility. To the extent that volatility is
persistent, this can induce a somewhat mechanical relation between Vega and future return volatility. In
contrast, RiskElasticity is a function of a continuum of volatility values and is therefore less susceptible to
producing such a mechanical relation.
70
next year is in the top or bottom decile of the cross-sectional returns distribution for that
year and zero otherwise.54
In contrast to stock return volatility, which captures changes in
a firm’s own returns over time, Extreme provides a comparison across firms. In addition,
by focusing on just the two tails of the cross-sectional distribution of stock returns, this
analysis provides a complementary measure of risk-taking behavior. (This intuition is
confirmed by the relatively low correlation between Volatility and Extreme, which,
although statistically significant, is only 0.34). We then estimate a logistic regression of
Extreme on the same independent variables used in previous tests and Volatility to ensure
that the specification captures the effect of risk-taking incentives on the tails and not just
on the variance of the return distribution.
The results are presented in Panel A of Table 10. Consistent with the determinants
of return volatility documented in Panel A and in prior studies, the first column shows
that relatively extreme stock returns have a strong negative relation with firm size and
prior operating performance (ROA) and a strong positive relation with volatility and stock
return. The second column adds controls for managerial risk aversion and managerial
risk-taking and stock price performance incentives measured as RiskElasticity and
PriceElasticity, respectively. We find that RiskElasticity exhibits a positive and
significant relation with relatively extreme stock returns in the next period. We also find
that both PriceElasticity and Age are negatively associated with extreme outcomes, which
is consistent with these variables capturing managerial risk aversion. The third column
54
Note that we use firm’s raw returns to calculate the extreme indicator rather than either industry-adjusted
or abnormal (e.g., Fama-French adjusted) returns because we (and most of the prior managerial risk-taking
literature) do not make the distinction between systematic and idiosyncratic risk in our analyses. See
Armstrong and Vashishtha (2011) for a discussion and analysis of the differential incentives that convexity
in managers’ payoffs provides with respect to systematic and idiosyncratic risk.
71
uses the traditional measures of managerial risk-taking and performance incentives (i.e.,
Vega and Delta, respectively) and shows that Delta exhibits a positive relation with
extreme stock returns but, somewhat surprisingly, Vega exhibits a strong negative
relation with extreme returns. This result is counterintuitive and is difficult to reconcile
with Vega capturing managerial risk-taking incentives. The final column includes all four
measures of equity incentives and we find that the coefficients of all four incentive
variables maintain the same sign and level of significance as when these variables were
included separately in the specification. This again suggests that RiskElasticity better
captures managers’ incentives to take extreme risk and, if anything, RiskElasticity and
Vega (and PriceElasticity and Delta) capture different dimensions of managerial risk-
taking incentives.
4.3.2. Implied Stock Return Volatility
As an alternative measure of risk-taking behavior, we use implied volatilities
derived from exchange-traded options prices. Implied volatilities are, by construction, the
market’s expectation of the firm’s average stock return volatility over option time to
expiration, and so provide a forward looking measure of market uncertainty, while
realized volatility measures are not forward looking. The use of standardized options
circumvents mechanical changes in implied volatility attributable to option expiration as
discussed in Patell and Wolfson (1981). We obtain implied volatilities from the
OptionMetrics Standardized Options Dataset. We use options of durations of 30 days,
although the main results are unaffected by including longer-dated options. Requiring
implied volatilities in the OptionMetrics database introduces sample attrition as
72
exchanged traded options are not available for all companies and are more frequent
among larger and more liquid firms. Table 10, Panel B, shows that RiskElasticity is
significantly associated with implied volatility (t-stat of 4.77). In contrast, Panel B also
reveals that the association between Vega and implied volatility is ambiguous, i.e., the
coefficient on Vega is only significant when RiskElasticity is included in the
specification. Moreover, when RiskElasticity is included in the model, the explanatory
power of the regressions increases from 33.89% to 45.55%, while including Vega in the
model is associated with a more modest increase in the explanatory power of the
regression (from 33.89% to 35.57%). We interpret these results as further evidence that
RiskElasticity is more powerful than Vega in terms of capturing managerial incentives to
take risk.
4.3.3. Research and Development Expenditures
Our next set of tests focuses on R&D investment, which is considered as a risky
decision by prior literature (e.g., Coles et al, 2006). Panel C of Table 10 presents the
results of a model of future R&D activity, which we estimate with a Tobit regression
given the substantial number of observations with zero R&D (60.46% of our sample).55
The first column considers only firm-level characteristics and, consistent with prior
studies (Coles et al., 2006), we find a strong positive relation between both firm size and
return volatility and future R&D expenditures. We also find that leverage, ROA, and the
equity book-to-market ratio exhibit a negative relation with future R&D (although the
55
Note that we report coefficients rather than marginal effects to facilitate our discussion of the statistical
significance of certain results. We also obtain similar results when we estimate the specification using OLS
and when we set missing values of R&D to zero.
73
coefficient on the book-to-market ratio is not significant at conventional levels). In the
second column, we find that RiskElasticity has a strong positive relation with future R&D
expenditures (t-stat of 4.00), which is consistent with RiskElasticity capturing managerial
risk-taking incentives. In the third column we replace RiskElasticity and PriceElasticity
with Vega and Delta, respectively. Consistent with Coles et al. (2006), we find a strong
positive relation between Vega and future R&D and a strong negative relation between
Delta and future R&D. The fourth column we include both RiskElasticity and Vega in the
specification and we find that the coefficients on both variables remain positive and
significant in the presence of each other, which again suggests that these two variables
could be capturing different dimensions of managerial risk-taking incentives. The last
column includes lagged R&D in the specification to determine how well the various
equity incentive measures explain annual innovations in R&D and to help control for
cross-sectional differences in R&D intensity across firms. We find that the coefficient on
RiskElasticity remains positive and highly significant, but Vega becomes statistically
indistinguishable from zero. Collectively, the results in Table 10 confirm the findings in
Table 8 and suggest that, compared to Vega, RiskElasticity is better able to explain cross-
sectional variation in alternative measures of risk-taking that are relevant for firms’
equity holders.
5. SENSITIVITY ANALYSES
The results of previous sections show that RiskElasticity has greater explanatory
power and exhibits stronger associations with a large number of realized and anticipated
74
measures of risk-taking behavior than Vega. The coefficient of Vega in some
circumstances is either statistically insignificant or has the opposite sign of what would
be expected if Vega measures risk-taking incentives. However, the previous tests rely on
specific assumptions about the functional form that determines the association between
risk-taking incentives and risk-taking behavior. We therefore assess the sensitivity of our
results to model specification to ensure that our results are not attributable to any
particular econometric assumption. Specifically, we analyze the potential effect of
correlated omitted variables, relaxing linearity assumptions, applying monotonic
transformations to the dependent and explanatory variables, controlling for industry
affiliation, and using alternative proxies for firm size. Finally, we also explore whether
RiskElasticity is sensitive to specific choices necessary for its numerical computation.
5.1. SENSITIVITY TO HIDDEN BIAS AND LINEARITY ASSUMPTIONS
The purpose of this paper is to develop and validate a new measure of managerial
risk-taking incentives rather than to provide causal evidence of the effects of managerial
risk-taking incentives per se. However, because endogeneity (typically in the form of
correlated omitted variables, such as managerial talent or risk aversion) is a concern with
any observational study (Rosenbaum, 2002), and with incentive compensation studies in
particular (Coles et al., 2006; Lewellen, 2006; Low, 2009), our analysis would be
incomplete without assessing the sensitivity of our inferences to correlated omitted
variables (e.g., managerial talent or risk aversion). One technique that more formally
acknowledges and addresses the endogenous relation between equity incentives and risk-
taking outcomes is a propensity-score matched pair research design coupled with a
75
sensitivity analysis (Rosenbaum and Rubin, 1986; Rosenbaum, 2002; Armstrong,
Jagolinzer, and Larcker, 2009). This technique involves modeling the conditional
probability of an executive receiving a particular level of risk-taking incentives given the
observable features of the executives’ contracting environments. Matched pairs of
observations with a similar conditional probability of receiving a given level of equity
(or, risk-taking) incentives (i.e., a similar propensity score) but a different level of actual
risk-taking incentives (i.e., observed Vega or RiskElasticity) are then formed.56
The
treatment and control firms (i.e., firms with relatively high and low RiskElasticity,
respectively) can then be compared to determine whether they differ in terms of the
outcome variables of interest (e.g., future return volatility). Finally, the sensitivity of any
significant differences in outcomes between the treatment and control firms can then be
assessed to determine the degree of “hidden bias” that would be necessary to alter the
statistical significance of the results. An additional benefit of propensity score matching
is that it is a nonparametric technique that is robust to nonlinearities, which also allows us
to further assess whether our previous inferences are robust to potential misspecification
of the functional form linking equity incentives to managerial risk-taking actions.
We first calculate the conditional probability of having a particular RiskElasticity
(i.e., our propensity score model) as a function of the control variables used in the
previous tests: cash compensation, managers’ age, firm size, equity book-to-market ratio,
leverage, and prior operating and stock price performance. We also include
56
It is important to note that this technique maximizes variation in the treatment variable (i.e.,
RiskElasticity) which can then be used to assess differences in various different outcome variables of
interest.
76
PriceElasticity and the managerial equity portfolio value (VPortf) when modeling the
predicted level of RiskElasticity to ensure that our results are not attributable to
differences in managers’ characteristics across the treatment and control groups.
The first set of results is presented in Panel A of Table 11 where we form matched
pairs of firm-years that have the most similar predicted RiskElasticity, but the most
dissimilar actual RiskElasticity.57
The variables below the dashed line (except, of course,
RiskElasticity) are the ones described above that are used to specify the propensity score
model and we find that the mean and median values are generally similar across the
treatment and control groups (Treat and Ctrl, respectively). This indicates that there is a
reasonable degree of covariate balance across the two groups and suggests that
differences in these variables across the two groups cannot be responsible for any
observed differences in outcome. We also find that the value of RiskElasticity is much
higher in the treatment group (mean and median values of 0.181 and 0.145, respectively)
than the control group (mean and median values of 0.056 and 0.042, respectively).
Although this result is to be expected since observations are formed as those with the
most dissimilar actual RiskElasticity values but the closest predicted values of
RiskElasticity, the highly economically and statistically significant differences across the
two groups suggests that there is maximum variation in RiskElasticity across the two
samples which will produce a powerful test of differences in outcomes.
The rows in the top half of Panel A (i.e., above the dashed line) compare mean
and median differences in outcomes across the treatment and control firms. We find that
57
We eliminate 5% of the matched pairs to improve the covariate balance across the subsamples of
treatment and control firms. Qualitatively, our inferences are not sensitive to this trimming procedure.
77
most of the statistically significant differences from our earlier tests continue to emerge
in this alternative research design. In particular, the first row shows that the treatment
firms (i.e., those with a relatively high RiskElasticity) have mean and median future
volatility of 0.547 and 0.488, respectively, while their matched counterparts (i.e., those
with a relatively low RiskElasticity) have a mean and median future volatility of 0.486
and 0.392, respectively. These differences are both economically and statistically
significant (t-stats of 2.24 and 3.23, respectively). Similar results obtain for most of the
other risk-taking measures and the mean and medians of the treatment distributions of the
other variables always lies to the right of its counterpart for the control group, and these
values are generally statistically significant.
Although the research design achieved a reasonable degree of covariate balance
for the observable variables, there is always the concern that “hidden bias” in the form of
unobservable correlated variables might be responsible for the observed difference in
future volatility (and other outcomes) across the two groups.58
We therefore calculate the
odds ratio of differential assignment to the treatment and control groups, or Г, that would
be necessary to reduce the statistical significance of the reported results to the 10% level.
For example, the value of Г = 1.8 for future R&D indicates that if there were a correlated
58
In our context, hidden bias exists if two executive (denoted i and j) have the same observed economic
covariates, but different probabilities (denoted ) of having a particular level of risk-taking equity
incentives. The odds that each executive was assigned to the high- and low-incentives category are denoted
i/(1–i) and j/(1–j), respectively. If the odds ratio (which we donate by Г, following Rosenbaum, 2002),
does not equal one, then the two executives have an unequal probability of being assigned to a category,
and hidden bias exists. Rosenbaum (2002) shows that relaxing the assumption that Г = 1 (which is the
maintained assumption in the tests for differences between the mean and median values of the two groups)
allows for a computation of the amount of hidden bias (or, the strength of a correlated omitted variable) that
is needed to alter any significant inferences. Smaller values of Г indicate statistically significant results that
are more sensitive to hidden bias.
78
omitted variable (e.g., executive risk tolerance) that caused executives with a higher
observed level of RiskElasticity to be assigned to the treatment group 64.3% of the time
and assigned to the control group only 35.7% of the time (conditional on all of the
variables in the propensity score model) rather than 50%/50% that is assumed by our
tests, a statistically significant difference in future volatility between the two groups
would still obtain. The relatively high values of Г indicate that the significant differences
in risk-taking outcomes across the two groups are relatively robust to hidden bias in the
form of correlated omitted variables.
We repeat the propensity score analysis in Panel B of Table 11 using Vega as the
treatment variable. Focusing first on differences in the variables from the propensity
score model (below the dashed line), we find that it is more difficult to achieve an
adequate degree of covariate balance. (This is not surprising given the high correlation
between Vega and firm size reported in Panel B of Table 7.) In particular, we find that
managers with higher Vega also tend to have higher Delta, equity portfolio value (VPortf)
and Cash Compensation, and are also older, work at larger firms that have more growth
opportunities (i.e., lower BM) and have had lower stock returns over the prior year. The
differences are all statistically (and arguably economically) different across the two
groups of firms with relatively high and low levels of Vega. These differences indicate
that it is difficult to achieve an adequate degree of covariate balance, which is indicative
overt bias and, more generally, identification problems (i.e., separately identifying the
effect of Vega on an outcome of interest rather than some other correlated variable, such
as delta or firm size). A comparison of Vega, however, reveals that its value is highly
79
statistically and economically different across the treatment and control groups, and
should therefore generate a powerful test of differences in outcomes.
Comparing the various outcomes across the firms with relatively high and low
values of Vega (above the dashed line), we find that the mean and median values of the
various risk-taking outcomes for the control firms (i.e., the firms with relatively low
Vega) are generally higher than their counterparts for the treatment firms (i.e., the firms
with relatively high Vega). Only future R&D and credit ratings (R&Dt+1 and Ratingt+1)
are higher in the sample of firm-years with relatively high Vega. Overall, these results are
difficult to reconcile with the notion that Vega is a powerful and robust measure of
managerial risk-taking incentives. Collectively, our results across both panels of Table 11
indicate that our earlier results for RiskElasticity are more robust to nonlinearities and
hidden bias (i.e., correlated omitted variables) than are those for Vega and that
RiskElasticity is a more versatile and powerful measure of managerial risk-taking
incentives according to a variety of common managerial risk-taking measures.
5.2. SENSITIVITY TO MODEL SPECIFICATION AND FUNCTIONAL FORM
To assess the sensitivity of our results to alternative specifications of the
functional form linking managerial risk-taking incentives to alternative measures of
future firm risk (i.e., return volatility and R&D investment), we repeat our earlier
analyses using the fractional ranked values of the independent variables. This
transformation of the independent variables also facilitates the interpretation of our
results since the coefficient estimates in this specification can be interpreted as relative
movement along the empirical cumulative distribution function (CDF) of those variables.
80
The first two columns of Panel A of Table 12 present results when the dependent variable
is one-year-ahead return volatility. The first column shows that the coefficient on
RiskElasticity is 0.286 (t-stat of 4.14). Similar to the results presented in Panel A of Table
8, the positive coefficient on RiskElasticity indicates that RiskElasticity captures
managerial incentives to increase firm risk. Moreover, since the independent variables are
fractionally ranked, the estimated coefficient of 0.286 on RiskElasticity indicates that
moving from the lowest to the highest value in our sample (i.e., moving from the zero
percentile to the one-hundredth percentile) implies an increase of 0.286 in future
volatility. In the second column, we find that the coefficient on Delta is negative and
significant (coefficient of –0.170 and t-stat of –2.72), but that on Vega is insignificant.
The negative sign of the coefficient on Delta in this alternative specification is not
consistent with the positive association between Delta and Volatilityt+1 reported in Table
8, Panel A. The sign and statistical significance of the coefficients on the remaining
control variables is identical across the two specifications in the first two columns and is
also largely consistent with their counterparts in Panel A of Table 8. This suggests that
although the signs and significance of the coefficients on RiskElasticity, PriceElasticity,
and the other control variables are robust to alternative specifications of their functional
relation with future volatility, the signs and significance of the coefficients on Vega and
Delta are not robust. This suggests that inferences based on Vega and Delta are sensitive
to research design choices in the model specification.
To determine whether these inconsistencies with the results of Table 8 are limited
to explaining return volatility, we repeat the test using R&D as an alternative measure of
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managerial risk-taking behavior. The last two columns of Panel A of Table 12 model
future R&D as a function of the ranked independent variables. In the third column, we
find that estimated coefficient on RiskElasticity is positive and significant (t-stat of 4.62).
This is again consistent with the results in Panel C of Table 8 and indicates that that the
relation between RiskElasticity and managerial risk-taking activities is robust to
alternative specifications of the functional form linking these two constructs. In contrast,
the last column of this table shows that the coefficient on Vega is negative and significant
(coefficient of –0.043 and t-stat of –4.36). This result is inconsistent with its counterpart
in Panel C of Table 8, and is at odds with the findings of Coles et al. (2006) and others.
Collectively, the results in Panel A of Table 12 indicate that RiskElasticity is robust to
alternative specifications to explain outcomes that are thought to reflect managerial risk-
taking activities but that Vega is not similarly robust. These results also suggest that
RiskElasticity might be more suitable as a measure of managerial risk-taking incentives
when the functional form of the relation between managerial equity incentives and
outcome variables of interest is, ex ante, unknown.
We next examine the effect of applying a monotonic transformation to the
dependent variable in the specification. In particular, we use the logarithm of future
volatility as dependent variable. The results of Table 12, Panel B, show that
RiskElasticity continues to exhibit a positive and significant relationship with the
dependent variable (t-stat of 4.98), Vega is not significantly associated with
log(Volatilityt+1) (t-stat of 0.63). In an untabulated analysis, we repeat this analysis using
the fractional ranked values of Volatilityt+1 as dependent variable and again find that the
82
coefficient on RiskElasticity is positive and significant but that the coefficient on Vega is
not significant.
Our next sensitivity analysis focuses on controlling for industry affiliation, which
is a well-known determinant of executive incentives-compensation practices. The results
of the second analysis are presented in the second group of two columns of Table 12,
Panel B and show the results when we include as a control the median return volatility in
fiscal year t for all firms in the same 2-digit SIC code.59
Thus, this variable controls for
both industry and year covariation in return volatility. The results in the third column
show that RiskElasticity continues to display a positive and relationship with future
returns volatility (t-stat of 2.09), but that the coefficient on Vega becomes insignificant (t-
stat of 0.53).
The final analysis in Table 12, Panel B, uses an alternative proxy for firm size,
since the scale of a firm’s operations has been shown to be an important first-order
determinant of managerial compensation and incentives (e.g., Smith and Watts, 1992;
Core and Guay, 1999; Baker and Hall, 2004). In particular, we use the natural logarithm
of total assets (logTA) rather than the natural logarithm of market value of equity as a
measure of size. In the fifth column of Table 12, Panel B, we find that RiskElasticity
continues to display a strong positive relationship with future returns volatility when
logTA is used as an alternative measure of firm size (t-stat of 6.82). In contrast, the last
column shows that Vega is unrelated to future return volatility (t-stat of –0.73). These
results show that Vega is sensitive to the measure of firm size and RiskElasticity is not.
59
We also repeated this analysis using the Fama andFrench (1997) industry classifications (with 12 and 48
groups) and obtained similar results.
83
This finding again highlights the identification problem that is inherent in Vega and
supports the idea that the highly significant correlation between Vega and firm size
makes it difficult to empirically separate the causal effects of each variable. Collectively,
the analysis of Table 12, Panel B, corroborates the results in Table 5, Panel A, and
indicates that RiskElasticity is robust to alternative functional forms, while Vega is not.
Some papers in the executive compensation literature use the natural logarithm of
Vega to account for the effect of skewness in the cross-sectional distribution of Vega
(e.g., Coles et al., 2006; Chava and Purnanandam, 2010). To explore the effects of this
transformation, in untabulated analyses we re-estimate the regressions in Table 2, Panel
A, using logarithmic transformations of RiskElasticity, PriceElasticity, Vega, and Delta.
The results are very similar to those reported in Table 8, Panel A, (the t-stat of
log(1+Vega) is reduced to 2.00). Unreported results also reveal that the coefficient on
log(1+Vega) is not significant when we apply a monotonic transformation of Volatilityt+1
(i.e., taking the natural logarithm or ranked values), which suggests that the skewness in
the distribution of Vega is not the only econometric problem faced by this variable.
5.3. SENSITIVITY TO VARIATIONS OF RISK ELASTICITY CALCULATION
Since RiskElasticity can be viewed as a more generalized measure of equity
incentives, it necessarily requires a number of assumptions (e.g., the range over which to
calculate the potential change in price and volatility). Our final analysis therefore
considers the sensitivity of our results to alternative assumptions for calculating
RiskElasticity. When calculating RiskElasticity, we have thus far assumed that there is no
relationship between variation in p and variation in . However, the moments of a firm’s
84
stock return distribution are likely to be correlated due to the natural risk-return tradeoff,
so managerial decisions that affect return volatility could also affect other moments of the
firm’s return distribution. Thus, a candidate measure of risk-taking incentives should be
robust to assuming alternative correlation structures between the expected value and
volatility of stock price. For example, one could assume lognormality of the return
distribution and model the relationship between expected returns (μ) and volatility ()
with the expression . However, assuming a specific type of correlation
is usually problematic (e.g., the previous expression imposes risk neutrality). To better
understand the effect that a potential monotonic relationship between risk and return
would have on the association between RiskElasticity and the outcome variables
considered in the previous section, we test whether our results are sensitive to various
restrictions on the support of p and Specifically, we restrict the support to those
combinations of (p, ) within a specified distance, from those points of the support
along the 45 degrees line: namely those such that p = . Thus, we restrict the values of p
and such that . We repeat our tests with values of from zero
to one and obtain results that are nearly identical to those reported in the previous section.
Specifically, the second column of Table 13 shows that taking the t-statistic of
the coefficient on RiskElasticity and the explanatory power of the regression are similar
to those when first column).
We also assess the sensitivity of our results by considering alternative ranges for
the support of both p and , namely,
85
(4)
We then estimate RiskElasticity and PriceElasticity with values of between zero
and two. The third column of Table 13 shows results restricting the support to values of p
and such that namely 0% ≤ p ≤ 50% and 0% ≤ ≤ 50%. The results are very
similar as in the benchmark case where Untabulated results indicate that
expanding the support to also produces similar results. Also, in additional
untabulated analyses we vary the density of the grid that is used to discretize the support
and observe no qualitative difference between using a grid of 10 x 10 versus 20 x 20.
Thus, RiskElasticity does not appear to be sensitive to alternative ranges of support or
alternative grid densities that are used for the numerical computation.
The measure RiskElasticity has thus far been estimated over the support p ≥ 0 and
≥ 0. However, depending on the manager’s risk aversion and the parameters of his or
her contract, it is possible that a manager would want to pursue a project with a negative
expected return, but a large expected volatility. For example, a manager with a high
degree of risk-tolerance and/or a highly convex payoff from his or her contract might
want to engage in a very risky strategy with a small expected loss (e.g., the initial
investment in R&D), as long as the potential upside makes up for the large potential
loss.60
To account for this possibility, we extend the support of rmgr to include negative
changes in p and and estimate RiskElasticity by integrating over the expanded support:
60
Another commonly cited example is risk-shifting in financially distressed companies, which benefits the
firm’s shareholders at the expense of the firm’s creditors.
86
(5)
Because, in the absence of considerations other than managerial equity incentives,
a manager would never rationally choose a strategy that yields rmgr < 0, we estimate
RiskElasticity integrating over the points in the support for which rmgr ≥ 0. The results
from this analysis are similar to those using the restricted support. In fact, both sets of
measures are highly correlated. Specifically, the fourth column of Table 13 shows that
using this alternative definition of RiskElasticity, we obtain t-statistics and R2 similar to
those in the benchmark case (first column).
As discussed above, RiskElasticity has three main advantages relative to Vega: (1)
it is based on returns rather than dollar value, (2) it is calculated using global rather than
local variation in volatility, and (3) it includes the effect of changes in stock price that
accompany changes in volatility as the result of the risk-return tradeoff. Although our
analyses have thus far demonstrated the collective importance of these features, we next
examine their individual importance to RiskElasticity. To do that, we scale Vega and
Delta by portfolio value (VPortf), and include those variables in the previous regressions.
The fifth column of Table 13 shows that the specification including scaled Vega explains
23.99% of the variation of Volatilityt+1, compared to the 19.44% explained by unscaled
Vega. In unreported analysis, we find that scaled Vega exhibits a relatively high
correlation with RiskElasticity (0.77) and performs similar to RiskElasticity when used in
its place in the tests reported in Table 8, Panel A. However, the results in Table 13 and
other untabulated tests similar to those in Table 8 also show that scaled Vega is inferior to
87
RiskElasticity in terms of describing risk-taking behavior, in terms of both statistical
significance and incremental explanatory power.
The last column of Table 13 presents results of similar tests when we calculate a
variant of RiskElasticity without including the cross-derivative of rmgr with respect to p
and . In other words, we calculate RiskElasticity integrating only along the axis. The
specification that uses this variant of RiskElasticity explains 25.01% of the variation in
future volatility compared to 25.57% for the specification that uses RiskElasticity. This
indicates that the cross-derivative of rmgr is able to explain a significant portion of the
variation in future stock return volatility. Untabulated results also reveal that the part of
the volume of rmgr that is due to the cross-derivative is positively correlated with future
volatility, which suggests that it also captures a portion of managers’ risk-taking
incentives. However, the results in Table 13 also suggest that the variant of RiskElasticity
that omits the cross-derivative of rmgr with respect to p and retains the desirable
empirical properties of RiskElasticity and produces similar empirical results.
The incentive measures used in the previous tests are averages across the top
executives of the firm (namely, those for whom we have public information regarding
their compensation contracts). We also test whether our inferences are sensitive to
measuring incentives taking only managerial compensation or taking the maximum
values of RiskElasticity and Vega among the top executives. Untabulated results reveal
that we obtain similar results with these alternative research design choices.
Using the information in the proxy statements under the new compensation
disclosure rules of 2006, we also examine whether our inferences are affected by
88
including unvested stock and unearned equity incentive plan awards in managerial
portfolios. In unreported analyses we find that including those components of the
compensation contract in the calculation of RiskElasticity produces similar inferences and
only a modest increase in t-statistics and explanatory power (i.e., R2).
We also compare RiskElasticity with Jensen and Murphy’s (1990) fractional
holdings measure of equity incentives in terms of their respective ability to describe
managerial risk-taking behavior. We find that the fractional holdings measure exhibits a
low correlation with RiskElasticity and is not significantly associated with future return
volatility when it is included together with RiskElasticity in the previous regressions.
Finally, to account for the possibility that managers might not fully understand all
dimensions of their compensation contracts (e.g., the time value of unexpired options),
we include a measure of portfolio sensitivity based on the intrinsic value (both in dollar
values and in returns) in the previous regressions. Although these variables are
significantly associated with future volatility, they cannot explain the association between
RiskElasticity and return volatility. In fact, these variables become insignificant or
weakly significant when RiskElasticity and PriceElasticity are included in the regression,
implying that executives seem to understand these features of their contracts and make
decisions accordingly.
6. CONCLUSION
This study proposes a new measure of managerial risk-taking incentives that is
based on the percentage change in the value of a manager’s equity portfolio for a
89
percentage change in stock return volatility, which we label “Risk Elasticity”
(RiskElasticity). This measure addresses at least three problematic features of equity
portfolio Vega, which is the traditional measure of risk-taking incentives that is used in
the empirical incentive compensation literature. First, RiskElasticity is based on returns
rather than the dollar change in value and is therefore less susceptible to cross-sectional
differences in managerial wealth. Second, RiskElasticity is “global” in the sense that it
measures the change in managerial wealth over a wide range of changes in stock return
volatility rather than small changes around a single point. Third, RiskElasticity accounts
for the effect of simultaneous changes in stock price and volatility on the sensitivity of
the manager’s portfolio to return volatility, which more accurately captures the risk-
return tradeoff that is inherent in most managerial risk-taking decisions.
We find that these features inherent in RiskElasticity result in a measure of
managerial risk-taking incentives that is empirically more descriptive than Vega. First,
we find that RiskElasticity exhibits a relatively modest correlation with equity portfolio
Vega and, in contrast to equity portfolio Vega, we find that RiskElasticity exhibits a low
correlation with firm size and managers’ equity portfolio value. Collectively, these
findings suggest that RiskElasticity captures a different dimension of managerial risk-
taking incentives than Vega and that RiskElasticity is less scale-dependent than Vega.
When we compare the explanatory power of RiskElasticity relative to Vega, we find that
RiskElasticity exhibits a stronger correlation and has much higher explanatory power than
Vega in explaining future firm risk and managerial risk-taking. We interpret these results
90
as evidence that RiskElasticity captures important dimensions or managerial risk-taking
incentives and is more descriptive of managerial behavior than the existing measures.
Although RiskElasticity is more empirically relevant for explaining various risk-
taking outcomes, it is admittedly more difficult to calculate than traditional measure of
risk-taking incentives (i.e., Vega) because of the required numerical simulations. A
relatively easy alternative that seem to account for some of the concerns inherent in Vega
is to scale Vega by the executive’s portfolio value. Although this simple transformation is
inferior to RiskElasticity, it does, to a large extent, eliminate cross-sectional differences in
equity-based compensation practices and yields a more “scale free” measure of
managerial risk-taking incentives.
Because RiskElasticity cannot address all the limitations of Vega that relate to the
unobservable nature of some managerial characteristics, the use of our measure is subject
to two caveats. First, similarly to Vega, RiskElasticity computations rely on the Black-
Scholes model, which assumes risk neutrality. However, because managers hold a
significant part of their wealth in their companies, this assumption might not be realistic.
Although, as shown earlier in the paper, RiskElasticity is likely to be less correlated with
unobserved heterogeneity in managerial risk aversion than Vega, our measure does not
fully correct for this unobservable source of cross-sectional variation. Second, the Black-
Scholes model assumes that the evolution of the firm’s stock price is exogenous.
Therefore, this model does not incorporate into the expected stock price the expected
incentive value of the executive’s equity-based compensation, which is one of the
primary reasons for using equity-based compensation. Thus, similarly to other empirical
91
measures not based on structural estimation, our measure is not free from simultaneity
concerns. That said, the results of this paper suggest that RiskElasticity is likely to be
more powerful than Vega in terms of describing the in-equilibrium association between
risk-taking incentives and risk-taking behavior.
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CHAPTER 3: SHAREHOLDER MONITORING AND RISK-TAKING INCENTIVES
1. INTRODUCTION
Convexity is a controversial property of corporate managers' compensation
contracts. Proponents of convex compensation contracts justify risk-taking incentives as a
way to reduce risk-related agency costs. Because managers have significant human
capital tied to the firm and are less diversified than outside shareholders, in the absence of
additional risk-taking incentives, they may pass up risky positive NPV projects. In
contrast, opponents of convex compensation contracts suggest that they provide
incentives for excessive risk-taking. Consistent with either view, previous empirical work
documents a positive association between risk-taking incentives and risk-taking behavior
(e.g., Rajgopal and Shevlin, 2002; Coles et al., 2006).
In this paper, we propose the idea that establishing the link between the shape of
compensation contracts and risk-taking behavior is incomplete without accounting for the
monitoring environment of the firm, because, in general, managers do not make decisions
that affect the firm's risk in isolation. In fact, significant claimholders on the value of the
firm, such as large shareholders, debtholders, and labor unions, often interfere in
managerial risk-taking decisions, such as investment in risky projects and acquisitions.61
61
Anecdotal evidence suggests that large shareholders interfere in managerial decisions that significantly
affect firm risk. The proposed acquisition by Charles River Laboratories (CRL) of WuXi PharmaTech and
the investment activity of CombinatoRx are two recent examples. On June 16, 2010, CRL's shareholder
Neuberger Berman (the owner of 6.26% of the company) opposed the proposed acquisition of WuXi
stating that it is "not in the best interest of shareholders based on the elevated financial and operational risks
it will bring to the company." In the fall of 2008, the CombinatoRx's large shareholder Biotechnology
Value Fund opposed the company's drug development activity stating that its "drug candidates are all high
risk and are best developed by larger companies with greater financial resources and a lower cost of
93
Even in the absence of direct interference, the threat of interference by a monitor can
force the manager to incorporate the monitor's preferences into the decision-making
process. We show theoretically and empirically that the firm's monitoring environment is
a significant determinant of the link between the shape of compensation contracts and
risk-taking decisions. Focusing on shareholder monitoring, we show that a tighter
monitoring environment mitigates the effect of contractual risk-taking incentives on risk-
taking behavior. While convexity of the manager's compensation contract is an important
driver of risk-taking behavior in firms with low shareholder monitoring, contractual
convexity has a significantly weaker effect in firms with high shareholder monitoring. In
addition, we provide evidence consistent with idea that boards, when deciding on the
managers' compensation contracts, take into account future shareholder interference in
the firm's risk-taking decisions.
The interaction between monitoring, incentives, and risk-taking is not obvious,
since it might depend on factors such as the preferences of the monitor and the manager
and the channel through which the monitor exerts influence on the manager. To
understand this interaction, we develop a stylized model that helps us derive empirical
predictions. We consider a firm run by a manager and owned by a large number of
minority shareholders and one large shareholder activist that interferes in the manager's
risk-taking decision. The manager needs to make an investment decision from a set of
risk-return pairs. Due to monitoring by the large shareholder, the investment decision
reflects both the preferences of the manager and those of the large shareholder. The
capital." (See Hedge Fund Solution's Catalyst Equity Research Report for the weeks ending July 16, 2010
and December 12, 2008, respectively)
94
degree of monitoring determines whether the investment decision reflects the preferences
of the manager or those of the large shareholder. In the absence of monitoring, the
manager would choose the investment decision that maximizes her expected utility,
which is determined by the shape of her compensation scheme and her intrinsic risk-
aversion. In contrast, in firms with high shareholder monitoring, the risk-taking decision
reflects the preferences of the monitor more than the preferences of the manager. Thus,
higher contractual risk-taking incentives have a higher impact on risk-taking behavior in
firms with lower levels of shareholder monitoring.
To see whether this first theoretical result is consistent with empirical evidence,
we examine whether the association between contractual risk-taking incentives of the
CEO and the risk-taking behavior of the firm changes with the degree of shareholder
monitoring. We employ three measures of the degree of shareholder monitoring: the
percentage of shares owned by dedicated investors (as defined by Bushee, 1998), the
percentage of shares owned by activists (as defined by Cremers and Nair, 2005), and the
percentage of shares owned by long-term investors. To measure the risk-taking behavior
of the firm, we use two variables: research and development (R&D) expenses of the firm
and idiosyncratic volatility of the firm's stock returns. We show that our first theoretical
result has broad empirical support. Specifically, we find that the positive effect of
contractual risk-taking incentives on risk-taking behavior is significantly lower for higher
values of shareholder monitoring. This result is consistent across different specifications.
Having established how the effect of risk-taking incentives is shaped by the
monitoring environment, we next examine whether this effect is taken into account by
95
firms' boards when designing managerial compensation contracts. To analyze this
question, we consider the following extension of the model. On the first stage, the board
decides on the convexity of the manager's compensation scheme with the goal of
maximizing the weighted average of the large shareholder's utility and the minority
shareholders' utility. The weight that the board places on the large shareholder's utility
can be interpreted as the degree with which the board is dominated by the large
shareholder. On the second stage, the large shareholder chooses the intensity with which
to interfere in the manager's risk-taking decisions. Finally, given the manager's
compensation scheme and the monitoring intensity of the large shareholder, the firm's
risk-taking behavior is determined. We show that to understand risk-taking incentives in
firms with different levels of monitoring, it is important to consider whether the large
shareholder can influence the board in choosing the shape of the manager's compensation
contract, or whether she can only influence managerial decisions. Specifically, if the
large shareholder does not control the board, the board adjusts for the large shareholder's
interference by ratcheting up the manager's contractual risk-taking incentives. In contrast,
if the monitor controls the board, the board optimally chooses a compensation contract
with lower risk-taking incentives in order to save the monitor the cost of interfering in
managerial decisions.
To see which of these two cases is more consistent with the data, we examine how
the degree of shareholder monitoring is associated with the contractual risk-taking
incentives of the manager. Because the large shareholder's influence over the board is not
observable and lies somewhere in the spectrum between complete control and no
96
influence, our analysis provides an empirical test for whether, on average, shareholder
monitoring determines the shape of compensation contracts. We find that there is a
positive and significant association between contractual risk-taking incentives and the
degree of shareholder monitoring. This result is consistent with the prediction of the
model for the case in which the large shareholder has little control over the board's
decisions regarding the shape of the compensation contract. Thus, our tests provide
indirect evidence that the effect of large shareholders on the firms' risk-taking behavior is
more related to their direct interference in risk-taking decisions, rather than to their
influence on the shape of the managers' compensation contracts.
Our paper is related to two strands of literature. First, it is related to the literature
that studies the link between the shape of managers' contracts and risk-taking behavior.
Tufano (1996) and Rajgopal and Shevlin (2002) provide industry-specific evidence that
managerial risk-taking behavior is positively associated with risk-taking incentives
provided by their options holdings. In a similar vein, Guay (1999) finds that firms' stock-
return volatility is positively associated with the convexity of managerial compensation
contracts. More recently, Coles et al. (2006) show that the shape of the compensation
contract has a significant effect on the manager's risk-taking behavior, measured by her
investment, financing, and diversification decisions. Also, Low (2009) documents that
the increase in the takeover protection in Delaware during the mid-1990s reduced
managerial risk-taking in firms whose managers had relatively flat compensation
contracts. We contribute to this literature by emphasizing that the link between the
97
managers' contractual risk-taking incentives and risk-taking behavior is affected by the
shareholder monitoring environment of the firm.
Second, our paper contributes to the literature that studies the role and impact of
large shareholders on firms' decisions. These questions are studied theoretically by
Admati et al. (1994), Burkart et al. (1997), Maug (1998), and others. On the empirical
side, previous literature shows that large shareholders can affect firms' operations through
multiple channels, including private negotiations (Carleton et al., 1998), hedge fund
activist campaigns (e.g., Brav et al., 2008; Klein and Zur, 2009), and "voting with one's
feet" (Parrino et al., 2003). These actions often affect the firm's risk: for example,
activists frequently oppose acquisitions. In a similar vein, Faccio et al. (2010) provide
evidence that corporate risk-taking behavior is affected by diversification of large
shareholders. Previous work also provides evidence of an association between
shareholder monitoring and the managers' compensation contracts. Specifically, Hartzell
and Starks (2003) find that institutional ownership concentration is positively associated
with the pay-for-performance sensitivity and negatively associated with the level of
executive compensation. However, this literature does not explore how shareholder
monitoring affects the link between the risk-taking incentives provided by compensation
contracts and managerial risk-taking behavior.
The remainder of the paper proceeds as follows. Section 2 presents a theoretical
model that examines the relation between risk-taking incentives and shareholder
monitoring. Section 3 discusses the sample, measurement of key variables, and the
research design used to test empirically the predictions of the model. Section 4 presents
98
the empirical results: (i) the effect of managerial risk-taking incentives decreases with the
level of monitoring, and (ii) CEOs of firms exposed to higher levels of shareholder
monitoring have more convex compensation contracts. Section 5 discusses robustness of
the empirical findings. Section 6 concludes.
2. THEORY AND EMPIRICAL PREDICTIONS
In this section we present a simple theoretical framework of endogenous choice of
risk by the corporate manager in the presence of shareholder monitoring. We develop
implications that are tested in the subsequent sections and discuss the underlying
intuition.
2.1. MODEL SETUP
Consider a firm owned by one large shareholder and a continuum of
infinitesimally small shareholders. To model risk-taking behavior, we follow the
approach of Stoughton and Zechner (2007). If the level of risk ζ² is chosen, then the firm
generates a one-time cash flow of
(1)
where ε is a random variable distributed with zero mean and unit variance. In order to
keep the model simple, we do not distinguish between market risk and idiosyncratic risk.
However, as we discuss later in this section, only idiosyncratic risk is relevant for the
argument presented here. As a result, one can think that ζ and refer to the
idiosyncratic risk of the firm and expected firm value, respectively.
99
Function is a reduced-form representation of the investment opportunity
set.62
We assume that is a strictly concave function with continuous first two
derivatives. These assumptions imply that the equilibrium level of risk-taking is uniquely
determined and smooth in the parameters of the model. In order to avoid corner solutions,
we assume that the marginal effect of additional risk-taking equals infinity when the
firm's risk is zero, , and minus infinity when the firm's risk is
infinite, . These assumptions ensure that the firm never wants to
avoid risk completely (i.e., choose ζ² = 0) or gamble as much as possible (i.e., choose ζ²
= ∞).
As in most modern corporations, the shareholders delegate the investment
decision to the manager, taking advantage of the manager's special skills and expertise.
Because the manager's utility function may be different from that of the shareholders
either due to an intrinsic difference in preferences with respect to the firm's risk or due to
non-linearity in the manager's compensation contract, the optimal investment policy for
the manager does not necessarily maximize firm value. In this paper, we posit that the
monitoring environment in the form of large shareholders affecting managerial actions
may be an important factor in the risk-taking behavior of the firm. Because shareholder
monitoring can take many different forms, we use a reduced-form way of modeling
shareholder monitoring instead of focusing on a specific form.63
62
By "investment" here we refer to a general class of investment activities, such as capital investment,
R&D, acquisitions, etc.
63 For example, shareholder monitoring can take active forms (i.e., direct intervention in the firm's
operations), such as behind-the-scene negotiations with the manager (e.g., Carleton et al., 1998) and
submission of shareholder proposals (e.g., Ertimur et al., 2010); as well as passive forms, such as
threatening to "vote with one's feet" (e.g., Admati and Pfleiderer, 2009; Edmans, 2009).
100
Specifically, we assume that the implemented risk policy is the weighted average
of the risk policy that maximizes the manager's utility from her compensation scheme and
the risk policy that maximizes the utility of the large shareholder:64
–
(2)
and
denote the risk policies that maximize the expected utilities of the manager
and the large shareholder, respectively. The idea of this reduced-form specification is
that, regardless of the form of shareholder monitoring, it ultimately affects decision
making through tilting it towards the preferences of the monitor. In (2), m [0,1]
captures the degree to which the large shareholder's preferences affect the risk-taking
decision of the manager. In one extreme case, if m = 0, then the presence of the large
shareholder has no effect on the manager's risk-taking strategy. In this case, the manager
chooses the investment strategy that maximizes the expected value of her compensation
scheme. In the other extreme case, if m = 1, then the risk-taking strategy is fully
determined by the preferences of the large shareholder.
To complete the setup of the model, we specify the utility functions of all players.
For simplicity, we assume that all utility functions have a mean-variance form, in which
the mean and the variance components are separable.65
Specifically, the expected utility
of the manager is
(3)
64
Alternatively, we could assume that the implemented risk policy maximizes the weighted average of the
manager's and the large shareholder's expected utilities. This specification leads to the same results, under
an additional restriction that concavity of function μ(⋅) does not change too rapidly.
65 This form of utility function endogenously arises when, for example, the values of claims held by all
players are normally distributed and their preferences have the constant absolute risk aversion property.
101
where parameters δ > 0 and v (–∞,∞) capture the sensitivity of the manager's utility to
the firm's performance and risk, respectively. Constant v can be positive or negative
depending on the manager's intrinsic risk-aversion and her contractual risk-taking
incentives. For example, if the manager's compensation scheme consists of a fixed salary
and the firm's stock, then v < 0, as the manager is risk-averse.66
In contrast, if the
manager's compensation scheme consists of a large number of stock options, then v > 0,
as the convexity of the manager's compensation scheme dominates her intrinsic risk-
aversion.
The expected utilities of the large shareholder and the minority shareholders,
normalized by the fraction of the firm held by each agent, are
(4)
(5)
where γ > 0 is the sensitivity of the large shareholder's utility function to firm risk. The
form of (4) compared to (5) implies that the large shareholder is less tolerant to risk than
the minority shareholders. Lower tolerance of the large shareholder may stem from
underdiversification (a large shareholder holds a significant portion of her assets in the
firm and thus is often underdiversified) and is consistent with empirical evidence (e.g.,
Klein and Zur, 2009; Faccio et al., 2010). From (4) and (5) it is clear why the
idiosyncratic risk, but not the market risk, is relevant for our argument. Even if
shareholders have different intrinsic risk-aversion, the ability to take any position in the
66
For example, if the manager has a CARA utility with the risk-aversion parameter of 2 and her
compensation scheme consists of 5% of the firm's stock, then the manager's expected utility is equal to
. Hence, δ = 0.05 and v= –2((0.05²)/2) = –0.0025.
102
market portfolio implies that in equilibrium their preferences with respect to a marginal
change in the firm's market risk are the same and are given by the market price of risk.
However, this is not true for idiosyncratic risk due to different diversification levels of
the large shareholder and the minority shareholders. While in the model we focus on the
case of γ > 0, the main empirical prediction of the model (prediction 1 in section 2.4)
does not depend on this assumption.
In the following section, we first solve the model assuming that all parameters
except ζ² are exogenous. Then, we consider the case when parameter v is chosen
endogenously by the firm's board.
2.2. RISK-TAKING FOR A GIVEN COMPENSATION SCHEME
Taking the first-order condition of (3) and (4), the equilibrium investment strategy
σ is given by
–
(6)
where ⋅ is the inverse function of ⋅ . By concavity of ⋅ , ⋅ is a decreasing
function. Intuitively, the firm takes less risk, if the manager or the large shareholder gets
more risk-averse.
Equation (6) relates the implemented risk-taking policy to parameters of the
manager's compensation scheme and the monitoring environment. To see how the degree
of interference by the large shareholder affects the firm's risk-taking strategy, we take the
derivative of (6) with respect to m:
(7)
This leads to the following proposition:
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Proposition 1. The monitoring environment affects the risk-taking strategy of the
firm. Specifically:
if – , then higher m decreases risk-taking of the firm;
if – , then higher m increases risk-taking of the firm.
Proof: Follows immediately from equation (7). ☐
Intuitively, the effect of higher monitoring depends on the relative tolerance of the
manager and the large shareholder to firm risk. Whether the manager prefers more or less
risk-taking than the large shareholder depends on her personal risk-aversion and the
shape of her compensation scheme. If the large shareholder is less tolerant to higher risk
than the manager ( – ) , then higher monitoring leads to less risk-taking as the
large shareholder pressures the manager not to accept risky projects. The opposite result
holds if the manager is very risk-averse and her compensation scheme is relatively non-
convex.
Our main empirical implication refers to the effect of the monitoring environment
on the link between the manager's contractual risk-taking incentives and risk-taking
behavior. Taking the derivative of (7) with respect to v, we get
(8)
Because ⋅ is negative,
is positive, meaning that the manager takes on more
risk if her contractual risk-taking incentives are higher. More importantly, we can see
from (8) that the derivative is affected by the degree of monitoring: higher monitoring
104
reduces the sensitivity of the firm's risk-taking to v. This result is formalized in the
following proposition:
Proposition 2. Conditional on the same δ and v,
is lower if m is higher.
Proof: Follows immediately from equation (8). ☐
Intuitively, other things being equal, higher monitoring implies that the
implemented risk policy is tilted toward the preferences of the large shareholder. Because
a marginal change in v affects the preferences of the manager but not those of the large
shareholder, the higher the monitoring parameter, the lower the effect of a change in v. In
order to provide further intuition, it is worthwhile to consider two extreme cases. If there
is no monitoring, then risk-taking is fully determined by the utility of the manager from
her compensation scheme. As a result, the effect of an increase in the contractual risk-
taking incentives is substantial. In the opposite case, if monitoring is perfect, then risk-
taking is fully determined by the preferences of the large shareholder. As a result, an
increase in the contractual risk-taking incentives of the manager has no effect on risk-
taking: regardless of her compensation scheme, the manager implements the decision that
is optimal for the large shareholder.
2.3. ENDOGENOUS MONITORING AND COMPENSATION
In this subsection, we extend the model by endogenizing the choice of v to
examine how the board reacts in designing the manager's compensation scheme when it
expects the large shareholder to interfere in the activity of the manager. Initially, the
board decides on the parameter v with the goal of maximizing the weighted average of
105
the large shareholder's utility and the minority shareholders' utility. The weight placed by
the board on the large shareholder's utility can be interpreted as the degree with which the
board is captured by the large shareholder. Then, the large shareholder chooses the
intensity m with which to interfere in the manager's risk-taking decisions, given the
manager's compensation contract. Because m is now endogenous, our results will link the
size of the large shareholder's ownership in the firm (block) α to contractual risk-taking
incentives v. Clearly, the large shareholder's sensitivity to risk γ in (4) is an increasing
function of her ownership α. For simplicity, we assume that .67
The choice of risk is given by (6). Assume that the monitoring
parameter m is chosen by the large shareholder to maximize her expected utility subject
to the cost function :
(9)
where satisfies standard conditions on the cost function.68
In addition, we assume
that c(m) is sufficiently convex: – for any m [0,1]. Let the
solution to (9) be denoted by .
Next, consider the board's choice of v. We consider two cases. In the first case,
the board is independent in the sense that it chooses v to maximize the value to minority
shareholders (5). To the extent that the marginal trader in the market is a minority
shareholder, this is equivalent to assuming that the board operates with the goal of
67
As argued in footnotes 5 – 6, this form of the utility function arises if the manager has a CARA
preference and the value of her claim is normally distributed. This specific modeling choice does not affect
the theoretical result of this section.
68 Specifically, it satisfies c(0) = 0, c′(⋅) > 0, c′′(⋅) > 0, limm→0 c′(m)=0, limm→1 c′(m)=∞.
106
maximizing the market value of the firm. In this case, v is chosen so that
, which implies that v is given implicitly as a solution to
(10)
In the second case, the board is captured by the large shareholder in the sense that
it chooses v to maximize the large shareholder's utility. In this case, v is chosen in order
to induce the manager to choose the risk-taking strategy that maximizes – .
Thus, the implemented v is equal to . The next proposition shows that the effect of
the large shareholder's block on the contractual risk-taking incentives is different in the
two cases:
Proposition 3. The effect of α on v depends on whether the board operates in the
interest of minority shareholder or the large shareholder:
(i) if the board operates in the interest of minority shareholders, then a
higher α is associated with a higher v in the manager's utility;
(ii) if the board operates in the interest of the large shareholder, then a
higher α is associated with a lower v in the manager's utility.
Proof: See Appendix A. ☐
Intuitively, more active monitoring by the large shareholder induces the manager
to forgo investment in risky projects. However, this is detrimental for the minority
shareholders, because the manager may pass up positive-NPV projects simply because
they are risky. If the board operates in the interest of minority shareholders, then the
board optimally adjusts for the expected interference by the large shareholder by
107
increasing the contractual risk-taking incentives of the manager. Thus, in this case, a
higher large shareholder's block is associated with higher contractual risk-taking
incentives. By contrast, if the board primarily takes into account the interests of the large
shareholder, then it optimally chooses lower contractual risk-taking incentives in order to
minimize the costs of interference. In this case, a higher size of the large shareholder's
block is associated with lower contractual risk-taking incentives, because a higher block
increases divergence of the risk preferences between the large shareholder and the
minority shareholders.
2.4. EMPIRICAL PREDICTIONS
The theory of risk-taking behavior in the presence of shareholder monitoring
outlined in this section leads to the following empirical predictions that we test in the
subsequent sections.
Our main empirical prediction is driven by the result of proposition 2. We call it
the main prediction, because it is independent of the preferences of the monitor. By
proposition 2, a higher m is associated with a lower . This translates into the
following empirical prediction:
Prediction 1. Higher shareholder monitoring is associated with a lower effect of
contractual risk-taking incentives on risk-taking behavior.
In addition to prediction 1, the model generates two other empirical predictions.
Unlike prediction 1, they are based on the assumption that the large shareholder dislikes
risk more than the minority shareholders. Endogeneity of v ensures that it is always the
case that . Even if the board operates in the interests of the large shareholder,
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the choice of v satisfies . If the board takes into account the utility of the
minority shareholders, the choice of v satisfies the strict inequality . Therefore,
as long as the large shareholder is less tolerant to risk than the minority shareholders and
the shape of the manager's compensation contract reflects the interests of at least some
shareholders, proposition 1 implies the following prediction:
Prediction 2. Higher shareholder monitoring is associated with lower risk-
taking.
The final empirical prediction deals with the choice of the manager's contractual
risk-taking incentives by the board that expects interference from the large shareholder:
Prediction 3. If the board operates in the interests of minority shareholders, then
a higher block of the large shareholder is associated with higher contractual risk-
taking incentives. If the board operates in the interests of the large shareholder,
then a higher block of the large shareholder is associated with lower contractual
risk-taking incentives.
These predictions do not depend on whether monitoring is exercised in an active
or passive manner. What is crucial for the interpretation of our model and empirical
results is that the presence of large shareholders has an influence on the manager's risk-
taking decisions. Even if the monitor never actively intervenes in the firm's operations,
the threat of intervention may be sufficient to constrain the manager.
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3. DATA AND EMPIRICAL APPROACH
In this section we describe the construction of our sample and the measurement of
risk-taking incentives and shareholder monitoring. Then we describe the empirical
approach used to test predictions 1 – 3 from section 2.
3.1. SAMPLE AND VARIABLE CONSTRUCTION
Our tests require data on executive compensation, institutional ownership, market
prices, and financial statements. Our primary sample consists of 25,322 firm-years from
2000 to 2007 and covers 5,207 individual firms. The sample is constructed as the
intersection of the following data files:
Equilar. We collect data on CEO compensation from Equilar, Inc. The Equilar file
contains detailed information about the board of directors and executive compensation
for 6,121 firms from 2000 through 2008.69
Thomson. We collect data on institutional ownership from the Thomson-Reuters
database of 13-F filings, otherwise known as CDA/Spectrum. The Spectrum data file
contains information on quarterly institutional holdings for all institutional investors with
$100 million or more under management.
CRSP/Compustat. We collect data on stock returns and equity prices from CRSP
and financial statement data from Compustat.
We measure incentives offered by the CEO's compensation scheme to alter the
firm risk (RiskIncentive) as the change in the dollar value of the executive's wealth for a
69
The Equilar file covers a larger cross-section of firms than the ExecuComp dataset, which includes only
the S&P 1500, but covers only a limited time period (from 2000 to 2008). Since we are interested in
generalizing our findings to the majority of publicly traded firms, we sacrifice time-series coverage to be
able to cover a wider cross-section of firms.
110
0.01 change in the annualized standard deviation of stock returns (vega) scaled by the
dollar value of the executive's portfolio.70
Because stock vega is very small for most
firms (Guay, 1999), we use the vega of the option portfolio to measure the total vega of
the stock and option portfolio.71
Similarly, we measure the contractual incentives to
increase the stock price value (ReturnIncentive) as the change in the dollar value of the
executive's wealth for a one percentage point change in stock price (delta) scaled by the
dollar value of the executive's portfolio. The vega and delta calculation follows Guay
(1999) and Core and Guay (2002), who use the Black-Scholes option valuation model
modified to account for dividends. The inputs of the Black-Scholes valuation model are
estimated as in Core and Guay (2002).72
We employ three measures of shareholder monitoring. First, we use the definition
of dedicated investors in Bushee (1998). According to Bushee (1998), dedicated investors
is the subgroup that has the strongest incentives to monitor the firm. Following Bushee
(1998), we construct our first proxy for shareholder monitoring, PctDED, as the
70
We scale by the dollar value of the executive portfolio to avoid scale effects (Edmans et al., 2009) and to
adjust for the potential influence of wealth-varying risk-aversion (Lambert et al., 1991).
71 This approximation is customary in the literature (e.g., Knopf et al., 2002; Rajgopal and Shevlin, 2002).
72 Option value is calculated as , where
. Delta and vega are the derivatives of the Black-Scholes value with respect to p and ζ,
respectively. As is customary in the corporate finance literature (e.g., Core and Guay, 2002), we measure
the inputs of the Black-Scholes formula as follows: p is the value of stock price at the end of the fiscal year
and ζ is the annualized return volatility (estimated as standard deviation of daily logarithmic stock returns
over the last 120 trading days before the fiscal year end date, multiplied by ). T is the remaining time
to maturity of the option in years, as of fiscal year end date, multiplied by 0.7 to account for early exercise.
X is the exercise price of the option, r = ln(1+risk-free interest rate), where the risk-free interest rate is the
yield, as of fiscal year end date, on a U.S. Treasury strip with the same time to maturity as the remaining
life of the stock option, and d = ln(1+expected dividend rate), where the expected dividend rate is set equal
to the dividends paid during the fiscal year by the year-end stock price. Also following previous literature,
we aggregate the values of all the securities owned by the executive in the current fiscal year, namely stock
options and stock holdings.
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percentage of the firm's shares owned by dedicated investors.73
Our second proxy for
shareholder monitoring PctACT is the percentage of the firm's shares held by institutions
classified as activists by Cremers and Nair (2005).74
While it is possible that activist
institutions do not monitor every firm in which they invest, monitoring is likely to
increase in the size of the stake held by activists. Finally, because long-term investors
have more ability to interfere in management decisions, we define a third measure of
shareholder monitoring as the percentage of shares owned by investors that have held the
firm's shares for at least 5 years.75
These three proxies map into variables m and α in the
model. On the one hand, conditional on her stockholding, a shareholder is likely to exert
more influence on managerial decisions if she is a dedicated investor, an activist, or a
long-term investor. On the other hand, these types of investors will have a greater
influence if they own a higher stake in the firm.
3.2. RESEARCH DESIGN
To test our main prediction, we estimate the following equation (firm subscripts
are suppressed for expositional convenience):
RiskTakingt+1 = α₀+α₁Monitoringt × RiskIncentivet + α₂Monitoringt +
α₃RiskIncentivet +θControlst +εt, (11)
73
Bushee's (1998) classification of investors is based on a factor analysis of the following institutional
investor characteristics: portfolio concentration, average percentage holdings, percent held in large blocks,
Herfindahl measure of concentration, stability of holdings (percent held for two years), portfolio turnover,
trading sensitivity to current earnings, average earnings change of firms bought vs. firms sold, and change
in holdings in firms with positive earnings vs. firms with negative earnings.
74 Cremers and Nair (2005) use the percentage of shares held by the 18 largest public pension funds,
arguing that public pension funds are known to be aggressive shareholder activists.
75 The Pearson (Spearman) correlations between these three proxies for shareholder monitoring range from
16% to 57% (27% to 69%).
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where RiskTaking is a proxy for risk-taking behavior and Monitoring is one of the three
proxies for shareholder monitoring described above: pctDED, pctACT and pctLT.
Following previous literature (e.g., Guay, 1999; Coles et al., 2006), we use two proxies
for risk-taking behavior. Our first proxy is the amount of investment in research and
development (R&D), scaled by total assets. R&D expenditures are typically viewed as
high-risk investments (e.g., Bhagat and Welch, 1995; Kothari et al., 2002). Our second
proxy for risk-taking behavior is the idiosyncratic return volatility of the firm's stock
measured over the firm's fiscal year end (IdVol).76
Firm risk summarizes the net effect of
all managerial risk-taking activities, including those that are not observed by the
researcher, and thus provides a complementary portrayal of managerial risk-taking
behavior. We focus on the idiosyncratic component of return volatility because, as we
discuss in the model, the shareholders' preferences may be different with respect to
idiosyncratic risk but are unlikely to be different with respect to market risk.77
Following previous literature (e.g., Core and Guay, 1999), we include the
following control variables in our analysis: Size is the natural logarithm of the firm's
equity market value measured at the end of the firm's fiscal year end; BM is the equity
book-to-market ratio; Leverage is total liabilities scaled by total assets; ROA is net
income scaled by total assets; Beta is the sensitivity of the firm's stock returns to market
fluctuations, estimated from the market model using daily return data over the fiscal year;
76
We obtain estimates of the idiosyncratic volatility as the standard deviation of the residuals in the
regression of daily returns on the value-weighted market return over 250 trading days prior to fiscal year
end multiplied by .
77 Consistent with this idea, untabulated results reveal that there is no evidence that shareholder monitoring
mitigates the effect of risk-taking incentives on firm's beta.
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IndustryVol is the median return volatility of all firms with the same 2-digit SIC code for
the current fiscal year; cash compensation (CashComp) and the sensitivity of the
manager's portfolio to stock return (ReturnIncentive) account for other characteristics of
the manager's contract. Because our measures of incentives are based on the risk-neutral
valuation framework, we include the CEO's Age and Tenure to control for the potential
confounding effect of managerial risk aversion. Assuming that the manager's total private
wealth is correlated with her wealth in the company (e.g., Bitler et al., 2005), we also
include the current value of the CEO's stock and option portfolio in the firm (VPortf) to
control for wealth effects on managerial behavior. Because return volatility is an input
used to estimate our proxy for contractual risk-taking incentives, we include current
volatility in (11) to ensure that our results are not driven by a mechanical relation
between return volatility and our measure of contractual risk-taking incentives. The main
prediction (prediction 1) suggests that α₁ in (11) is negative. Prediction 2 suggests that
higher Monitoring is, on average, associated with higher RiskTaking.
To test prediction 3, we examine whether boards rationally anticipate the effect of
monitoring on contractual risk-taking incentives captured in equation (11) by ratcheting
up the convexity of the CEO's contract. We specify the model as follows:
RiskIncentivet = β₀+β₁Monitoringt + θControlst + εt , (12)
where all the variables are as defined before. If the board operates in the interests of
minority shareholders, then prediction 3 suggests that β₁>0. If the board is dominated by
the large shareholders in deciding on the shape of the CEO's compensation scheme, then
prediction 3 suggests that β₁<0.
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Table 14 presents descriptive statistics for the sample and the variables used in the
analysis. Panel A shows that the sample spans many sectors of the economy and has an
industry distribution that is similar to CRSP/Compustat, which mitigates sample selection
concerns. Panel B reports descriptive statistics for the variables that we use in our tests.
The mean (median) market capitalization for the sample is $3.28 ($0.45) billion, which is
larger than the $2.39 ($0.23) billion for the CRSP/Compustat sample. The sample
captures 64.05% of the market capitalization of all firms on the CRSP/Compustat file
with data over the sample period. The CRSP/Compustat sample includes 10,867 firms, so
our sample covers nearly 50% (5,207) of the firms with complete market and accounting
data in the sample period.
4. EMPIRICAL RESULTS
The results of the risk-taking behavior analysis are presented in Table 15.
Consistent with prediction 1, we find that the positive association between contractual
risk-taking incentives and risk-taking behavior is significantly lower for firms with higher
shareholder monitoring. When the dependent variable is research and development
(R&D), all our proxies for shareholder monitoring show a significant negative interaction
with the measure of contractual risk-taking incentives (the t-statistics of the coefficients
on the variables PctDED, PctACT, and PctLT are –3.02, –4.73, and –3.67, respectively).
In the idiosyncratic volatility (IdVol) regressions, we find similar results: the interaction
between our proxies for shareholder monitoring and the measure of contractual risk-
taking incentives is always significantly negative (the t-statistics of the coefficients on the
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variables PctDED, PctACT, and PctLT are –2.16, –4.58, and –2.68, respectively). This
effect is also economically significant. For example, one standard deviation from the
mean in PctDED reduces the coefficient on RiskIncentive in the R&D regression by
approximately 10%.
Consistent with the previous literature, our proxy for contractual risk-taking
incentives shows a positive association with the dependent variables in all three panels.
We also find that the three proxies for shareholder monitoring (PctDED, PctACT, and
PctLT) are negatively associated with future R&D (t-statistics of –4.35, –2.01, and –8.15,
respectively) and with idiosyncratic volatility (t-statistics of –1.82, –1.80, and –2.80,
respectively). This finding is consistent with prediction 2 in the model, which states that
shareholder monitoring is associated with lower risk taking.
In terms of the control variables, only Age shows a consistent and significant
association with both proxies for risk-taking behavior (IdVol and R&D), which is
consistent with the notion that older CEO's are more risk averse because of retirement
plan concerns (e.g., Sundaram and Yermack, 2007). The negative relation between risk-
taking behavior and both ReturnIncentive and CashComp is consistent with previous
research (e.g., Knopf et al., 2002; Coles et al., 2006). With respect to firm characteristics,
Size shows a strong positive association with future R&D, but a negative association with
future IdVol. In contrast, we find that Leverage exhibits a weakly positive association
with future IdVol and a negative association with R&D. Finally, the negative association
between ROA and IdVol and R&D suggests that firms react to poor performance by
engaging in more risk-taking behavior. Overall, the results of Table 15 are consistent
116
with the notion that higher shareholder monitoring mitigates the effect of contractual risk-
taking incentives on risk-taking behavior.
Table 16 presents the results on the cross-sectional determinants of contractual
risk-taking incentives. Consistent with prediction 3 for the case in which the board
operates in the interests of minority shareholders, we find a robust positive association
between shareholder monitoring and risk-taking incentives (RiskIncentive). Specifically,
all the proxies for shareholder monitoring are significantly associated with the measure of
contractual risk-taking incentives (the t-statistics of the coefficients on the variables
PctDED, PctACT, and PctLT are 2.46, 5.33, and 2.12, respectively). From the results of
Table 16, we also observe that the sensitivity of the CEO's portfolio to changes in stock
prices (ReturnIncentive) and stock volatility (RiskIncentive) are positively associated,
which is not surprising given that stock options affect both characteristics. In terms of the
control variables, the results of Table 16 suggest that boards introduce more risk-taking
incentives in the manager's contract in firms that operate in more volatile environments
(IndustryVol). Also, the results of Table 16 show that portfolio convexity has a negative
association with profitability (ROA) and Size, and a positive association with Leverage,
which is consistent with the idea that higher contractual risk-taking incentives are more
common among risky firms. Overall, the results of Table 16 support the notion that
boards adjust for shareholder interference by ratcheting up managers' contractual risk-
taking incentives.
The results in Table 16 are consistent with the idea that it is less costly for activist
shareholders to influence managers' actions directly than to pursue their own interest by
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trying to influence board decisions. First, the recent controversy related to the proxy
access and "say-on-pay" regulation implies that activist shareholders were not satisfied
with their influence on boards.78
In the sample period, U.S. shareholders did not have a
direct vote on executive pay, and although a few companies had voluntarily adopted non-
binding "say-on-pay" measures, the vast majority had not. Alternatively, shareholders
could influence executive compensation through shareholder proposals and vote-no
campaigns. However, voluntary adoption of non-binding proposals by the firm is low
(Ertimur et al., 2010). Although vote-no campaigns have led to significant reduction in
CEO pay, they are rare.79
Finally, survey evidence suggests that activist institutions
prefer direct negotiation to proxy proposals due to the difficulty of persuading other
institutions to agree on unified proxy strategies (Useem et al., 1993). The previous
arguments notwithstanding, there is also evidence that shareholders' opinions can have a
bearing on board decisions related to compensation (Hartzell and Starks, 2003). To what
extent large shareholders are able to impose their preferences in the board room is an
empirical question.
5. ROBUSTNESS
5.1. MATCHED PAIR DESIGN
There are two important limitations of the traditional linear regression approach
used in the preceding tests. First, this approach relies on a linear functional form linking
78
The term "proxy access" (popularly labeled as "shareholder democracy") in the recent regulatory debate
is related to the idea that shareholders may require the corporation to include in the proxy statement a
director (or slate of directors) nominated by shareholders to run against incumbent board members.
79 Ertimur et al. (2010) find 134 vote-no campaigns in the period between 1997 and 2004.
118
the outcome variables of interest (i.e., IdVol and R&D) with both the independent
variable of interest (i.e., interaction between shareholder monitoring and contractual risk-
taking incentives) and control variables (e.g., firm size, leverage, profitability, etc.). If the
linearity assumption is violated, the model is misspecified and could produce biased
parameter estimates. Second, to the extent that there is endogenous matching of managers
and investors with firms (and compensation contracts) on the basis of some unobserved
characteristics (e.g., the manager's risk aversion or talent), there is a traditional correlated
omitted variable problem. Endogeneity can be addressed using two-stage procedures
through the identification of appropriate instruments. However, given that our research
question addresses the interaction of two variables, an instrumental variable approach
could not be implemented in this setting without making controversial assumptions.80
In order to mitigate these econometric concerns, we utilize a propensity score
matched pair research design (Rosenbaum, 2002). Since a matched pair research design is
typically nonparametric, it relaxes the assumption that there is a linear relation between
the independent and control variables and the outcome variables. A matched pair design
also enables us to assess the sensitivity of our results to the presence of unobserved
correlated omitted variables. Following Rosenbaum (2002), we determine the magnitude
of the correlated omitted variable bias that is necessary to cause any statistically
significant differences between matched pairs to become insignificant. While this
80
Because there could be unobserved characteristics that determine both shareholder monitoring and
compensation contracts, these approaches would require the identification of two instruments that are
correlated with the independent variables of interest but uncorrelated with the error term in the model. If
choosing a single instrument is often problematic because it requires making assumptions about the
exogenous nature of the instrument (e.g., see Larcker and Rusticus, 2010), choosing two instruments in this
setting would be even more problematic and could not be done without controversy. In addition,
approaches based on instrumental variables continue to rely on linearity assumptions.
119
approach does not resolve the endogeneity problems, the computation enables us to
provide some insight into whether our results are robust to endogenous matching.
The research question analyzed in this paper differs from the usual matched pair
design because the treatment of interest in this case is the interaction between two
variables: shareholder monitoring and contractual risk-taking incentives. To address this
additional complexity, we implement a variation of the usual propensity score matching
methodology. First, we form a treatment group and a control group based on the
propensity to adopt different levels of contractual risk-taking incentives. This procedure
produces a treatment group wherein firms have a significantly higher level of contractual
risk-taking incentives than their control pairs but similar values of the covariates. We
expect to observe a higher level of risk-taking behavior in the treatment group. Next, we
assess whether there is a significant difference between the results in pairs with different
levels of shareholder monitoring in the treatment and the control observations.
Specifically, we divide the matched pairs into two groups. The first group is formed by
those pairs in which the treatment observation has a higher level of shareholder
monitoring than its matched control pair. Conversely, we include in the second group
those pairs in which the treatment observation has a lower degree of shareholder
monitoring than the control observation. If shareholder monitoring reduces the effect of
contractual risk-taking incentives, we expect to observe that the difference in risk-taking
behavior between the treatment and control samples will be higher in the second group;
namely, in those pairs in which the firm with higher contractual risk-taking incentives
(the treatment observation) is also subject to lower monitoring.
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We estimate the propensity to award contractual risk-taking incentives using an
ordered logistic model for quintiles of RiskIncentive as a function of firm and CEO
characteristics. With these propensity scores, we obtain the treatment and control samples
using a non-bipartite matching algorithm suggested by Derigs (1988).81
Following
previous research (e.g., Armstrong et al., 2010), we eliminate the 10% of the pairs with
the largest difference in propensity scores in order to improve the covariate balance
between the treatment and control groups.82
Table 17, Panel A, indicates that the
differences in covariate values are statistically or economically insignificant, providing
evidence that the control variables are balanced across the matched pairs. Table 17, Panel
A, also shows that the treatment group has significantly higher values of contractual risk-
taking incentives (RiskIncentive) than the control group, which is consistent with the
matching procedure forming two groups with variation in the treatment variable and
balance in the covariates. Finally, Panel A also reveals that the treatment group exhibits
higher levels of risk-taking behavior (measured by R&D and IdVol) than the control
group. Even without using measures of shareholder monitoring in the matching
algorithm, we observe that the treatment group has higher values of PctDED, PctACT,
81
Derigs' algorithm is optimal in the sense that it considers the potential distances between other pairs
when forming a particular matched pair. The distance between each pair is estimated as the squared value
of the difference between the propensity scores of both observations divided by the square of the difference
in the values of the treatment variable.
82 Untabulated results reveal that our inferences are not sensitive to this trimming procedure.
121
and PctLT than the control group. This is consistent with the idea that firms with higher
shareholder monitoring grant their managers more convex contracts.83
A formal test of the difference in risk-taking behavior between matched pairs is
presented in Table 17, Panel B. It shows that in the subsample in which the treatment
observations are subject to lower monitoring than their matched pairs (ΔShrMonit < 0),
the values of future IdVol and R&D are higher if RiskIncentive is higher. In contrast, in
the subsample in which the treatment observations are subject to higher monitoring than
their matched pairs (ΔShrMonit ≥ 0), there is no consistent evidence that firms with more
contractual risk-taking incentives engage in significantly more risk-taking behavior. For
the pairs in which ΔShrMonit < 0, these differences in risk-taking behavior between the
two subsamples are highly statistically significant. For example, using PctLT as a proxy
for shareholder monitoring, the t-statistics for the difference in means is –36.54 for IdVol,
–10.52 for R&D. Panel B also shows similarly strong results for the median values of
those differences.
Table 17, Panel B, shows that the results for the subsample where ΔShrMonit < 0
exhibit low sensitivity to hidden bias. For example, a value of 6.1 in the parameter Γ
means that the results remain statistically significant to the existence of a correlated
omitted variable that shifts the assignment of managers to the treatment group from a
50% / 50% probability of being assigned to the treatment and control groups to a 86% /
83
These results are not very strong, because we did not use shareholder monitoring measures in the
matching algorithm. In untabulated results we find that using shareholder monitoring as a treatment
variable leads to substantial differences in RiskIncentive between the treatment and control groups.
122
14% probability assignment.84
In contrast, the sensitivity results for the subsample
ΔShrMonit ≥ 0 confirm that there does not seem to be a significant difference between
the treatment and control groups, and, in some cases, the difference is in the opposite sign
as that in the ΔShrMonit < 0 subsample.
5.2. OTHER ROBUSTNESS CHECKS
To assess the robustness of our results to measurement error, we re-estimate
equations (11) and (12) using a naive measure of the convexity of the manager's contract,
namely, the number of stock options owned by the executive divided by the total number
of securities owned by the executive in the company. With this simple measure, we are
able to replicate the results of the nine tabulated regressions except for one, which
implies that our results are not restricted to a particular measure of contractual risk-taking
incentives. We also analyze whether our results are sensitive to the specific definition of
our proxies for shareholder monitoring. Specifically, we re-estimate equations (11) and
(12) and obtain similar inferences with a number of variations of our measures for
shareholder monitoring, such as the number of activists (as defined in Cremers and Nair,
2005), the number of blockholders (institutions that hold 5% or more of the company's
shares), the percentage of shares owned by institutional investors that own more than 1%
of the firm and invested in the company for at least two years, and the average holdings
84
In our context, hidden bias exists if two executives (denoted i and j) have the same observed covariates,
but different probabilities (denoted π) of having a particular level of convexity. The odds that each
executive was assigned to the treatment and control groups are denoted πi/(1–πi) and πj/(1–πj), respectively.
If the odds ratio (following Rosenbaum (2002), denoted by Γ, does not equal one, then the two executives
have an unequal probability of being assigned to a category and hidden bias exists. Rosenbaum (2002)
shows that relaxing the assumption that Γ = 1 allows for a computation of the amount of hidden bias (or,
the strength of a correlated omitted variable) that is needed to alter any significant inferences. Smaller
values of Γ indicate statistically significant results that are more sensitive to hidden bias.
123
of blockholders that owned stock of the company for at least five years. The Pearson
correlation coefficients between these alternative measures and the three proxies for
shareholder monitoring used in the paper range from 16% to 71%.
To further explore the robustness of our results, we test the interaction between
contractual risk-taking incentives and proxies for other types of monitoring to analyze
whether the interaction reported in Table 15 is due to the effect of other constraints on the
CEO's actions. Prior literature has shown that various governance characteristics are
related to firms' compensation practices (Core et al., 1999). We therefore re-estimate
equation (11) including governance variables that are used in prior research. In particular,
previous studies linking corporate governance to compensation practices examine two
broad categories of governance constructs: board characteristics and antitakeover laws.85
We find that these governance variables generally have a significant interaction with
contractual risk-taking incentives. However, those interactions are unable to subsume the
effect of shareholder monitoring on risk-taking incentives documented in this paper. We
also include in the regressions free cash flow (estimated as operating cash flow minus
depreciation scaled by total assets) to control for agency problems within the firm. Our
results are unaffected by the inclusion of those additional control variables.
85
We use three variables to capture board characteristics and antitakeover provisions: (i) the percentage of
independent directors on the board, (ii) an indicator that equals one if the CEO is also the chairman of the
board, and (iii) the governance index proposed by Gompers et al. (2003). We obtain these data from
Equilar and Thompson.
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6. CONCLUSION
This study generates two insights regarding the connection between shareholder
monitoring and risk-taking incentives provided by managers' compensation contracts.
First, shareholder monitoring mitigates the effect of contractual risk-taking incentives on
risk-taking behavior. Second, boards rationally anticipate this effect and offer
compensation contracts that adjust for the deterring effect of shareholding monitoring on
the manager's risk-taking behavior. We show theoretically that the effect of shareholder
monitoring on risk-taking incentives of the CEO's contract critically depends on whether
the monitor can impose her will on the compensation committee's decisions.
We design empirical tests to investigate the predictions of the model. Using a
variety of measures and research design choices, we demonstrate that the effect of
contractual risk-taking incentives decreases with the level of shareholder monitoring. We
also show that a robust positive empirical relation exists between the level of the CEO's
contractual risk-taking incentives and shareholder monitoring. These findings are
consistent with the notion that it is easier for shareholders to influence managerial actions
than board decisions. Our results have implications for the ongoing debate on the optimal
level of risk-taking incentives in executive compensation contracts. In particular, our
results suggest that, when evaluating risk-taking incentives provided by a compensation
contract, it is important to account for the monitoring environment to which the firm's
management is exposed.
125
APPENDIX A: VARIABLE DEFINITIONS
Risk oversight variables
ROindex Index formed by adding the value of the 25 dichotomous variables defined based on the 25 data
items in the GMI dataset. Each of the 25 variables that equal one if the answer to the question is
“yes”, and zero otherwise. See Appendix B.
RCIndex Index formed by adding the data items related to the characteristics of the risk committee (GMI
dataset). See Appendix B.
ERM Indicator variable that equals one if the firm has comprehensive disclosures in Enterprise Risk
Management (ERM) policies, and zero otherwise (GMI dataset). See Appendix B.
CRO Indicator variable that equals one if the firm has a Chief Risk Officer (CRO) or similar position,
and zero otherwise (GMI dataset). See Appendix B.
RMstd Indicator variable that equals one if the firm adheres to a risk-management charter or standard, and
zero otherwise (GMI dataset). See Appendix B.
Other Index formed by adding the data items related to other types of Risk Oversight provisions (GMI
dataset). See Appendix B.
Incentives and Executive characteristics
PriceElasticity Average return on the manager’s equity portfolio due to a range of increases in stock price up to
100% (Equilar).
RiskElasticity Average return on the manager’s equity portfolio due to a increases in stock volatility up to 100%
adjusting for returns on the manager’s equity portfolio due to increases in stock price (Equilar).
Vega Average Vega of the portfolio of the company’s top executives estimated as in Core and Guay
(2002), measured in millions (Equilar).
Delta Average Delta of the portfolio of the company’s top executives estimated as in Core and Guay
(2002), measured in millions (Equilar).
RiskIncentive Sensitivity of the CEO’s stock and option portfolio to stock–return volatility. Estimated as the
Vega of the CEO’s portfolio scaled by the value of the CEO’s stock and option portfolio in the
firm. Vega is the change in Black–Scholes value (in millions of dollars) of the CEO’s equity
portfolio resulting from a one percent change in the annualized standard deviation of the
firm’s stock return (Equilar)
ReturnIncentive Sensitivity of the CEO’s stock and option portfolio to stock price. Estimated as the Delta of
the CEO’s portfolio scaled by the value of the CEO’s equity portfolio in the firm. Delta is the
change in Black–Scholes value (in millions of dollars) of the CEO’s equity portfolio resulting
from a one percent change in the firm’s stock price (Equilar)
CashComp Average cash compensation of the company’s top executives (Equilar).
Age Average age of the company’s top executives measured in years (Equilar).
Proxies for shareholder monitoring
PctDED Number of shares owned by dedicated investors scaled by total shares outstanding. Dedicated
investors are defined as in Bushee (1998) (Thompson)
PctACT Number of shares owned by activists scaled by total shares outstanding. Activists are defined
as in Cremers and Nair (2005) (Thompson)
PctLT Number of shares owned by institutions that held the company’s shares for at least five years
scaled by total shares outstanding (Thompson)
126
Dependent variables
IdVol Standard deviation of market-adjusted daily returns over 250 days prior to fiscal year end (CRSP)
Beta Coefficient in a regression of daily returns on the market return over 250 days prior to fiscal year
end (CRSP). Both firm and market returns are adjusted for the risk-free rate.
Implied Volatility Average implied volatility measured over the fiscal year using options with 30-day expiration
(OptionMetrics)
Extreme Indicator variable that equals one if the firm’s annual compounded return is in the bottom and top
decile of all the firms with non-missing Compustat and CRSP data in that fiscal year, and zero
otherwise.
ExtremeRet Indicator variable that equals one if the firm’s annual compounded return is in the bottom and top
quartile of all the firms with non-missing Compustat and CRSP data in that fiscal year, and zero
otherwise.
ExtremeROAdj Indicator variable that equals one if the firm’s industry-adjusted ROA is in the bottom and top
quartile of all the firms with non-missing Compustat and CRSP data in that fiscal year, and zero
otherwise.
ExtremeROA Indicator variable that equals one if the firm’s change in ROA with respect to the previous year is
in the bottom and top quartile of all the firms with non-missing Compustat and CRSP data in that
fiscal year, and zero otherwise.
Allindrawn Average all-in-drawn spread of the bank loans in the fiscal year. All-in-drawn spread is the spread
charged by the bank over LIBOR for the drawn portion of the loan facility (Loan Pricing
Corporation database), measured in basis points.
Rating S&P Credit Rating, which ranges from 1 to 21, with low values corresponding to lower credit
ratings (Compustat).
Control variables
Size Natural logarithm of market value (CRSP).
BM Book-to-market ratio (CRSP and Compustat).
ROA Return on assets; operating income scaled by total assets (Compustat).
Return Annually compounded return using daily stock return data (CRSP).
Leverage Total liabilities divided by total assets (Compustat).
PctInstit percentage of stock of the company owned by institutions (Thomson).
Volatility Annualized standard deviation of daily returns measured over the fiscal year (CRSP).
IndustryVol Median value of Volatility of all the firms in the same 2-digit SIC code (CRSP).
Dealamount Average amount of the bank loans in the fiscal year (Loan Pricing Corporation database).
Maturity Average Maturity period (in months) of the bank loans in the fiscal year (Loan Pricing Corporation
database).
Secured Indicator variable that equals one if loan facility/bond is secured with collateral, and zero otherwise
(Loan Pricing Corporation database).
127
APPENDIX B: THE RISK OVERSIGHT INDEX
This appendix presents the variables used to construct the risk oversight index. These data were collected
from a sample of 1,701 public firms. The information comes from public disclosures: SEC filings and
corporations’ websites.
# Description
Risk Committee
#1 Has the board adopted a separate committee or subcommittee responsible for oversight of risk
management?
#2 If the board has adopted a separate committee or subcommittee responsible for oversight of risk
management, is a majority of such committee independent?
#3 Does at least one non-executive member of the risk committee have expertise in risk management?
#4 Do the non-executive members of the risk committee with expertise in risk management form a
majority of the members of that committee?
#5 Is the chair of the risk committee non-executive, with expertise in risk management?
#6 Does at least one non-executive member of the risk committee have recent expertise in risk
management?
#7 Do the non-executive members of the risk committee with recent expertise in risk management form
a majority of the members of that committee?
#8 Is the chair of the risk committee non-executive, with recent expertise in risk management?
#9 Does at least one non-executive member of the risk committee have substantial industry knowledge?
#10 Do the non-executive members of the risk committee with substantial industry knowledge form a
majority of the members of that committee?
#11 Is the chair of the risk committee non-executive, with substantial industry knowledge?
#12 Does at least one non-executive member of the risk committee have substantial industry knowledge
and expertise in risk management?
#13 Do the non-executive members of the risk committee with substantial industry knowledge form a
majority of the members of that committee?
#14 Is the chair of the risk committee non-executive, with substantial industry knowledge?
#15 Does at least one non-executive member of the risk committee have substantial industry knowledge
and expertise in risk management?
#16 Do the non-executive members of the risk committee with substantial industry knowledge and
expertise in risk management form a majority of the members of that committee?
128
#17 Is the chair of the risk committee non-executive with substantial industry knowledge and expertise in
risk management?
#18 If the board has adopted a separate committee or subcommittee responsible for oversight of risk
management, does such committee have a written charter or terms of reference?
#19 If the board has adopted a separate committee or subcommittee responsible for oversight of risk
management, has such committee engaged or does it have the power to engage experts independently
of corporate management?
#20 If the board has adopted a separate committee or subcommittee responsible for oversight of risk
management, does such committee undertake annual evaluations of its performance as a committee?
Enterprise Risk Management (ERM)
#21 Does the company make comprehensive disclosures of its enterprise risk management policies
(ERM) in its annual report, or in other publicly available sources?
Chief Risk Officer or similar position
#22 Is someone at the company specifically tasked with risk management?
Policy and standards
#23 Does the company adhere to (or state that it has implemented) a nationally or internationally
recognized risk management charter or standard, such as AS/NZS 4360, COSO's Integrated
Framework for Enterprise Risk Management, or something comparable?
Other organizational structure
#24 If the company has a committee or subcommittee charged with risk management oversight (whether
or not it is a separate committee) does the charter of the committee or subcommittee (or other
governance document) provide such committee or subcommittee with a comprehensive set of
responsibilities and powers to conduct adequate oversight of enterprise-wide risk?
#25 Does the committee or subcommittee charged with risk management oversight (whether or not it is a
separate committee) have independent access to the risk officers of the company?
129
APPENDIX C: LEGISLATIVE EVENTS RELATED TO RISK OVERSIGHT
This appendix presents a brief description of recent legislative events related to risk oversight.
Event
Number Legislative Event Date Content
#1 Introduction of Shareholder Bill of
Rights Act (Sen. Schumer) 5/19/2009
- Independence of chairman of the board
- Shareholder vote on executive compensation
- Proxy access
- Majority voting
- No staggered boards (mandatory annual elections)
- Risk Committee
#2
Introduction of Corporate
Governance Reform Act (Sen.
Ellison)
7/21/2009
- Independence of chairman of the board
- Shareholder vote on executive compensation
- Risk Management Committee and Chief Risk Officer
- Independence and duties of the Compensation Committee
- Director certification (to be studied by SEC)
130
APPENDIX D: FIGURES
Figure 1. Graphical Depiction of Equity Portfolio Risk Elasticity
This figure depicts the RiskElasticity of a hypothetical equity portfolio. RiskElasticity is the average return
of a manager’s equity portfolio (rmgr) produced by increases in stock volatility , adjusting for the
accumulated return rmgr induced by increases in stock price p holding constant at 0. p and are the
firm’s stock price and the firm’s stock volatility, respectively, and p0 and 0 are the initial values of p and
, respectively.
O=(p0,
0)
p
F=(2p0,
0)
rmgr
G=(2p0, 2
0)
E=(p0, 2
0)
C
D
131
Figure 2. Examples of Risk Elasticity
Panel A
Panel B
Panel C
Panel D
Panel A and B present two plots of the RiskElasticity and PriceElasticity surface for two executives for the
2006 fiscal year. Panel A plots the surface for the CEO of Celebrate Express Inc. (Kevin A. Green) and
produces a RiskElasticity of 1.282 and a PriceElasticity of 1.148. Panel B plots the surface for the CEO of
Aspreva Parrmaceuticals Corp. (Richard M. Glickman) and produces a RiskElasticity of 0.008 and a
PriceElasticity of 0.508. Panel C and B present a comparison between Celebrate Express Inc. (dashed line)
and Aspreva Parrmaceuticals Corp. (solid line) along the %price increase axis (panel C) and the %
volatility increase axis (panel D).
132
APPENDIX E: PROOFS
Proof of Proposition 3. First, consider the case of the board operating in the
interests of minority shareholders. Then, the optimal level v is such that
₀ (13)
Taking the first-order condition of (9) and using (13), we obtain that the
equilibrium level of monitoring m satisfies
₀
₀ ′ (14)
Plugging (14) into (13), we obtain the following equation, which links the large
shareholder's block α with the equilibrium level of monitoring:
′ ₀ ₀ (15)
The left-hand side of (15) is an increasing function of m, which ranges from 0 for
to ∞ for . Therefore, (15) has a unique solution for any α. Because ⋅ is
a decreasing function, the right-hand side of (15) increases in α. Therefore, the solution to
(15) is an increasing function of α. Taking the full derivative of (13), we obtain
₀
₀
₀
′
(16)
Because ⋅ , both terms in the sum are positive. Thus, because the
equilibrium monitoring increases in α, an increase in α leads to an increase in v. Hence, if
the board operates in the interests of minority shareholders, then higher α is associated
with higher v.
133
Second, consider the case of the board operating in the interests of the large
shareholder. Then, the optimal level of v is ₀ , since in this case the interests of
the manager and the large shareholder are aligned, so the large shareholder does not need
to interfere in the risk-taking decisions of the firm. As a result, a marginal increase in α
leads to a marginal decrease in v:
₀ .
134
APPENDIX F: TABLES
Table 1. Descriptive statistics
This table presents descriptive statistics for firms in the sample. Panel A reports the industry distribution of
sample observations and the components of the risk oversight index (ROindex) measured in 2008,
following the Fama and French (1997) industry classification. The last two columns report the number of
companies with ROindex > 0 and ROindex = 0, respectively. Panel B reports the number of companies with
a Risk Oversight Index (ROindex) greater than n (1 ≤ n ≤ 5) in a given year. Panel C reports descriptive
statistics for the main variables used in the statistical tests, measured from 2000 to 2008. See Appendix A
for variable definitions.
Panel A. Industry distribution
Fama-French
Industry Group
RC
RMstd
CRO
ERM
Other
ROindex>0
ROindex=0
Business Equipment 1 4 14 5 35 53 230
Chemicals 0 1 2 1 6 8 43
Consumer Durables 0 2 4 2 8 15 30
Energy 0 1 12 4 11 25 58
Healthcare 3 3 9 4 24 34 96
Manufacturing 4 5 19 6 27 49 138
Finance 47 6 101 61 82 151 171
Consumer Non Durables 2 1 14 5 21 35 65
Wholesale & Retail 4 3 14 2 24 42 148
Telecomunications 1 0 6 1 9 14 29
Utilities 6 0 27 13 21 39 33
Other 2 5 22 7 31 58 137
Total 70 31 244 111 299 523 1,178
Panel B. Time-series distribution
Fiscal year ROindex>0 ROindex>1 ROindex>2 ROindex>3 ROindex>4 ROindex>5
2000 141 52 17 14 10 5
2001 159 60 22 18 13 8
2002 216 85 30 24 19 15
2003 301 107 40 29 22 18
2004 346 120 53 42 31 24
2005 364 128 66 53 39 31
2006 383 133 73 55 42 33
2007 399 144 84 63 48 39
2008 523 175 100 72 56 46
135
Panel C. Distributional statistics
ROindex>0 (523 firms)
ROindex=0 (1,178 firms)
t-test
Compustat-
CRSP
Variable Mean Median Std Mean Median Std p-value Median
IdVol 0.37 0.31 0.22 0.39 0.34 0.22 0.000 0.46
Beta 1.03 0.97 0.54 1.09 1.03 0.56 0.000 0.77
Rating 12.87 13.00 3.23 12.43 13.00 3.14 0.000 12.00
All-in-drawn 107.14 75.00 95.68 120.46 95.00 100.05 0.000 137.50
Size 7.74 7.59 1.58 7.38 7.28 1.54 0.000 5.47
BM 0.57 0.49 2.27 0.52 0.44 0.92 0.050 0.56
Leverage 0.25 0.23 0.21 0.22 0.20 0.20 0.000 0.16
ROA 0.08 0.07 0.10 0.09 0.09 0.12 0.009 0.04
Return 0.13 0.08 0.59 0.16 0.08 0.66 0.010 0.01
PctInstit 0.69 0.72 0.23 0.71 0.75 0.23 0.000 0.37
Cash 0.86 0.58 1.11 0.71 0.53 0.77 0.000 0.39
Delta 0.54 0.16 2.05 0.72 0.15 5.39 0.038 0.07
Vega 0.06 0.02 0.10 0.05 0.02 0.09 0.001 0.01
Age 53.84 53.60 9.95 53.40 53.40 4.69 0.001 52.60
136
Table 2. Association analysis before the 2007-2008 financial crisis
This table reports results for estimating equity risk as a function of risk oversight. Panel A presents results
of the association between the risk oversight index (ROindex) and proxies for firm equity risk from 2000 to
2006. Panel B presents results of the association between risk oversight and three measures of performance
extremeness. Panel C presents results of the association between risk oversight and proxies for firm credit
risk. See Appendix A for other variable definitions. t-statistics are based on standard errors clustered by
firm and year to correct for time-series and cross-sectional dependence, respectively (see Gow et al., 2010).
***, **, and * denote statistical significance at the 0.01, 0.05, and 0.10 levels (two-tail) respectively.
Panel A. Risk oversight and equity risk
LogIdVol Beta
Variable coef t-stat coef t-stat
Constant –0.72*** –4.63 1.27*** 3.14
ROindex –0.01** –2.58 –0.01* –1.90
Size –0.11**** –6.38 0.01 0.29
BM –0.00 –0.31 –0.13** –2.21
Leverage 0.00 0.00 –0.54*** –4.16
ROA –0.34** –2.54 –1.10*** –3.96
Return 0.08*** 3.01 –0.02 –0.65
IndustryVol 1.36*** 14.72 0.32** 2.32
PctInstit –0.08 –1.17 0.62*** 10.42
Cash –0.00 –0.27 0.02 1.44
Delta –0.00 –0.14 0.00 0.24
Vega 0.23*** 2.73 –0.13 –0.83
Age –0.00 –0.92 –0.01** –2.24
Adj R2 55.60% 15,72%
N 10,230 10,230
137
Panel B. Risk oversight and credit risk
Allindrawn Rating
Variable coef t-stat coef t-stat
Intercept 290.55*** 5.52 Omitted
ROindex –2.09** –2.11 0.06* 1.72
Size –16.44*** –9.09 0.93*** 15.11
BM –10.04 –1.35 0.46*** 2.98
Leverage 86.04*** 7.04 –1.61*** –5.24
ROA –132.52*** –6.66 3.92*** 4.52
Return 16.09*** 3.10 –0.75*** –3.51
IndustryVol –7.82 –0.75 1.32** 2.35
PctInstit –44.86*** –3.29 –2.61*** –7.42
Cash 3.55** 1.97 –4.91*** –6.07
Delta 1.21 0.93 –0.08 –1.12
Vega 14.19 0.93 –0.01 –0.84
Age –1.05* –1.75 –0.10 –0.20
Volatility 146.56*** 8.27 0.10*** –7.28
Dealamount –4.23** –2.30
Secured 73.46*** 13.48
Maturity 10.34*** 3.55
Adj R2 52.65% 17.09%
N 3,720 5,419
Panel C. Risk oversight and extreme outcomes
ExtremeRet ExtremeROAadj ExtremeROA
Variable coef t-stat coef t-stat coef t-stat
Constant –0.70* –1.74 0.79 1.41 –0.49 –0.90
ROindex –0.05* –1.83 –0.08*** –2.84 –0.09*** –5.50
Size –0.01 –0.44 0.01 0.23 –0.10*** –2.63
BM 0.12** 2.27 –0.08 –1.23 –0.27* –1.74
Leverage –0.05 –0.39 –0.34 –1.50 –0.92*** –5.41
ROA 0.24 0.51 1.27** 2.21 1.60*** 2.72
Return 0.70*** 7.58 –0.10* –1.81 0.00 0.02
IndustryVol –1.07*** –4.94 1.08*** 4.98 –0.18 –0.82
PctInstit 0.75*** 2.99 0.30** 2.11 0.92*** 5.65
Cash –0.02 –1.30 0.04 1.24 0.00 –0.04
Delta 0.00 0.82 0.01 0.75 0.01 1.36
Vega 0.15 0.41 0.53 1.35 0.29 0.71
Age –0.02*** –3.60 –0.04*** –5.83 –0.01 –0.63
Volatility 4.09*** 8.64 1.09** 2.53 2.98*** 6.38
Adj R2 9.66% 4.22% 8.44%
N 10,230 10,230 10,228
138
Panel D. Index decomposition
Financial firms Non-Financial firms
LogIdVol LogIdVol LogIdVol
Variable coef t-stat coef t-stat coef t-stat
Constant –0.72*** –4.66 –0.96*** –4.29 –0.62*** –3.60
RCindex –0.01** –2.53 –0.01* –1.73 –0.01 –0.68
CRO –0.03 –0.93 –0.01 –0.39 –0.04 –0.69
ERM –0.08** –1.99 –0.05 –1.12 –0.07* –1.66
RMstd –0.07* –1.67 0.06 0.60 –0.11** –2.07
Other 0.00 –0.03 0.03 1.63 -0.01 –0.56
Size –0.11*** –6.35 –0.12*** –7.65 –0.11*** –5.72
BM –0.00 –0.30 0.09 1.61 –0.01 –0.48
Leverage –0.00 –0.06 –0.14** –2.21 0.03 0.70
ROA –0.35*** –2.63 0.22 0.71 –0.47*** –4.03
Return 0.08*** 3.02 0.10*** 5.52 0.08*** 3.16
IndustryVol 1.36*** 14.85 2.48*** 11.68 1.23*** 15.14
PctInstit –0.08 –1.17 –0.01 –0.17 –0.14** –2.11
Cash 0.23*** 2.64 –0.02 –1.63 –0.01 –0.73
Delta 0.00 -0.14 0.40** 2.23 0.19** 2.12
Vega 0.00 -0.04 0.02*** 2.63 0.00 –0.44
Age 0.00 -0.92 –0.01** –1.97 0.00 –0.90
Adj R2 55.65% 49.93% 53.84%
N 10,230 1,879 8,351
Panel E. Regression analysis using matched pairs
This panel reports results for estimating equity and credit risk as a function of risk oversight using the same
controls used in equations (1), (2), and (3).
DepVart = ROindext + β Controlst + εt
t-statistics appear in parentheses and are based on standard errors clustered by firm and year to correct for
time-series and cross-sectional dependence, respectively. ***, **, and * denote statistical significance at
the 0.01, 0.05, and 0.10 levels (two-tail) respectively. See appendix A for variable definitions. Coefficients
and t-stats for control variables are omitted.
Dependent
Variable (DepVar)
Coeff of
ROindex () t-stats (Pseudo)R2 N
LogIdVol –0.014** –2.25 52.04% 4,461
Beta –0.007 –1.35 12.69% 4,461
Extreme returns –0.057** –2.25 15.95% 4,461
Extreme ROAadj –0.083** –2.05 30.44% 4,461
Extreme ROA –0.018*** –2.74 7.99% 4,414
Credit Rating 0.068** 2.16 18.15% 3,002
All-in-drawn –1.942* –1.87 64.12% 1,700
139
Table 3. Time-series analysis before the 2007-2008 financial crisis
This table presents results from estimating the time-series association between risk oversight structures and firm risk.
In Panel A, RiskOversight is defined as the value of the risk oversight index (ROindex) at the end of the sample period.
DimplRO is an indicator variable that equals one if ROindex > 0 in that fiscal year, and zero otherwise. In Panel B and
C, RiskCommittee is defined as the value of RCindex at the end of the sample period. DimplRC is an indicator variable
that that equals one if RCindex > 0 in that fiscal year, and zero otherwise. Panel B presents the results using the GMI
sample and panel C presents the results using a control sample from CRSP-Compustat matched on propensity score.
Coefficients and t-statistics for the intercept and control variables are ommitted. Other r.o. (risk oversight) subdindexes
refers to CRO, ERM, RMstd, and Other (see appendix A). t-statistics are based on standard errors clustered by firm and
year to correct for time-series and cross-sectional dependence respectively. ***, **, and * denote statistical
significance at the 0.01, 0.05, and 0.10 levels (two-tail) respectively.
Panel A. Implementation of risk oversight structures
Dependent variable
LogIdVol (GMI sample)
LogIdVol
(Matched sample)
Independent variables coef t-stat coef t-stat
RiskOversight 0.02*** 2.70 0.03*** 2.91
RiskOversight*DimplRO –0.03*** –3.13 –0.04*** –2.98
DimplRO –0.00 –0.01 0.01 0.19
Controls Included Included
Adj R2 55.52% 51.10%
N 10,230 4,461
Panel B. Implementation of the risk committee. GMI sample.
Dependent variable LogIdVol ExtremeRet Allindrawn
Independent variables coef t-stat coef t-stat coef t-stat
RiskCommittee 0.01 1.29 0.00 0.00 –1.16 –1.30
RiskCommittee*DimplRC –0.02* –1.87 –0.17** –2.53 –11.11*** –3.36
DimplRC –0.02 –0.37 0.87** 3.11 42.35** 3.05
Other r.o. subindexes Included Included Included
Controls Included Included Included
Adj or Pseudo R2 55.67% 9.74% 52.78%
N 10,230 10,230 3,720
Panel C. Implementation of the risk committee. Matched sample.
Dependent variable LogIdVol ExtremeRet Allindrawn
Independent variables coef t-stat coef t-stat coef t-stat
RiskCommittee 0.01 1.33 –0.02 –0.46 –3.02* –1.74
RiskCommittee*DimplRC –0.02** –1.98 –0.25** –2.54 –8.92*** –2.77
DimplRC –0.02 –0.48 1.22*** 2.88 36.85** 2.40
Other r.o. subindexes Included Included Included
Controls Included Included Included
Adj or Pseudo R2 51.07% 10.89% 50.83%
N 4,461 4,461 1,700
140
Table 4. Stock market performance during the 2007-2008 financial crisis
This table presents results from estimating cross-sectional differences in the market performance of non-
financial firms with different degree of risk oversight. Panel A shows the results of regressing daily returns
from the period 8/1/2007 to 3/31/2009 on the risk oversight index (ROindex) and risk factors. Panel B
presents the results of the same regressions on days when the market return was lower than –1%. The
matched sample includes the 268 pairs corresponding to non-financial firms that had ROindex > 0 in the
period 2000-2006, and their matched pairs. The dependent variable is daily return adjusted by the risk-free
rate. Mktrf is the market return adjusted by the risk-free rate. SMB, HML and UMD are the size, book-to-
market, and momentum factors. Standard errors are clustered by day. ***, **, and * denote statistical
significance at the 0.01, 0.05, and 0.10 levels (two-tail) respectively. Returns are expressed in %.
Panel A. Difference in returns from August 2007 to March 2009
GMI sample Matched sample
Variable coeff t-stat coeff t-stat coeff t-stat coeff t-stat
Intercept 0.033** 2.30 0.033** 2.33 0.022 1.30 0.025 1.44
ROindex –0.001 –0.21 –0.002 –0.39 0.005 0.75 0.002 0.37
Mktf*ROindex –0.010** –2.49 –0.021*** –5.60
Mktrf 1.065*** 114.43 1.069*** 109.17 1.068*** 101.31 1.087*** 93.24
SMB 0.573*** 19.68 0.573*** 19.68 0.490*** 13.37 0.490*** 13.37
HML
–
0.093*** –2.69 –0.093*** –2.69 –0.081** –2.00 –0.081** –2.00
UMD
–
0.133*** –7.31 –0.133*** –7.31 –0.119*** –5.57 –0.119*** –5.58
N 575,854 575,854 205,440 205,440
R2 33.22% 33.23% 29.16% 29.18%
Panel B. Difference in returns on days when the market return was below –1%
GMI sample Matched sample
Variable coeff t-stat coeff t-stat
Intercept 0.011 0.20 –0.020 –0.31
ROindex 0.035*** 3.68 0.071*** 7.19
Mktrf 1.064*** 44.68 1.077*** 44.48
SMB 0.516*** 9.81 0.394*** 6.04
HML –0.145*** –3.20 –0.160*** –3.21
UMD –0.168*** –6.73 –0.156*** –5.03
N 157,001 55,852
R2 20.45% 19.65%
141
Table 5. Market reaction to legislation related to risk oversight
This table presents results from estimating the market reaction to various events related to the legislation of risk oversight. Panel A presents results from an analysis of cross-sectional differences in the market reaction to legislation related to risk oversight using all firms in the GMI dataset. Panel B presents results of the same tests using pairs matched on propensity score (see Appendix D). Events are
as defined in Appendix B. NoRiskOversight is an indicator variable that equals one if ROindex=0, and zero otherwise. NoRiskCommittee is an indicator variable that equals one if RCindex = 0, and zero
otherwise. NoCRO is an indicator variable that equals one if CRO = 0, and zero otherwise. NoERM is an indicator variable that equals one if ERM = 0, and zero otherwise. NoRMstd is an indicator variable that equals one if RMstd = 0, and zero otherwise. NoOther is an indicator variable that equals one if Other = 0, and zero otherwise. Staggered is an indicator variable that equals one if the firm
has a staggered board provision and zero otherwise. ExcessPay is the natural logarithm of total annual pay for the CEO measured in millions, less the natural logarithm of median pay in that year for all
firms in the same Fama-French industry group and size quintile. NLargeInstit is the natural logarithm number of institutions holding at least 1% of shares outstanding. NCoalitions is the natural log of one plus the number of possible small institutional investor coalitions that would collectively control 1% or more of shares outstanding. IsChair is an indicator variable that equals one if the CEO or any
other insider is also chairman of the board, and zero otherwise. Size is the natural log of market value, BM is the ratio of book value to market value, and Momentum is the market adjusted return over
the prior six months. Heteroskedastic-robust t-statistics appear in parentheses. ***, **, and * denote statistically significance at the 0.01, 0.05, and 0.10 levels (two-tail) respectively. t-test test for difference in means, and Wilcoxon (Wlx) test for difference in medians.
Panel A. Market reaction to legislation related to risk oversight. All GMI firms.
Cross-sectional regressions
on event days Difference in coefficients on
event and non-event days
Event #1 Event #2 Pooled Mean (t-test) Median (Wlx)
Intercept 0.73 –0.50 –3.40*** –5.43*** –1.39** –3.03*** –2.21 –3.93 –2.19 –3.70 (0.71) (–0.35) (–3.61) (–4.40) (–1.95) (–3.12) (–0.84) (–1.22) (–1.01) (–1.36)
NoRiskOversight 0.22 0.41** 0.32*** 0.35 0.32*
(1.23) (2.45) (2.62) (1.51) (1.81) NoRiskCommittee 0.97* 1.63*** 1.31*** 1.33* 1.32**
(1.88) (3.01) (3.42) (1.84) (2.06)
NoCRO 0.22 0.20 0.22 0.25 0.19 (0.91) (0.74) (1.19) (0.78) (0.97)
NoERM 0.64 0.55 0.61** 0.61 0.61*
(1.63) (1.54) (2.28) (1.50) (1.77) NoRMstd –0.09 –0.13 –0.11 –0.07 –0.11
(–0.14) (–0.26) (–0.28) (–0.18) (–0.28)
NoOther –0.26 0.18 –0.04 –0.02 –0.03 (–1.22) (0.96) (–0.28) (–0.14) (–0.09)
Staggered –0.05 –0.05 0.05 0.06 0.00 0.01 0.02 0.02 0.03 0.03
(–0.35) (–0.30) (0.36) (0.39) (0.04) (0.10) (0.12) (0.17) (0.24) (0.32) ExcessPay 0.25*** 0.27*** 0.00 0.02 0.12*** 0.14*** 0.09 0.11 0.09 0.11
(2.90) (3.03) (0.03) (0.44) (2.63) (3.04) (0.88) (1.11) (0.83) (1.01)
NLargeInstit 0.05 –0.02 0.15 0.12 0.11 0.05 0.12 0.06 0.11 0.06 (0.17) (–0.08) (0.67) (0.52) (0.58) (0.26) (0.27) (0.15) (0.44) (0.26)
NCoalitions –0.06 –0.05 0.20** 0.19** 0.07 0.07 0.10 0.10 0.08 0.07
(–0.58) (–0.51) (2.05) (2.00) (0.93) (0.95) (0.97) (0.96) (0.79) (0.79)
IsChair –0.09 –0.09 –0.09 –0.08 –0.09 –0.08 –0.09 –0.09 –0.09 –0.08
(–0.50) (–0.50) (–0.58) (–0.53) (–0.73) (–0.71) (–0.59) (–0.57) (–0.85) (–0.79)
Size –0.08 –0.06 0.14** 0.17** 0.04 0.06 0.10 0.12 0.12 0.13 (–1.11) (–0.83) (1.98) (2.32) (0.76) (1.15) (0.51) (0.61) (0.71) (0.89)
BM 0.02 0.01 –0.01 –0.01 0.01 0.00 –0.00 –0.01 –0.01 –0.02
(0.76) (0.39) (–0.36) (–1.06) (0.46) (–0.19) (–0.02) (–0.12) (–0.30) (–0.54) Momentum 0.64** 0.57* 0.24 0.18 0.28 0.22 0.97 0.90 0.50 0.45
(2.06) (1.86) (1.12) (0.89) (1.54) (1.26) (0.61) (0.57) (1.49) (1.36)
N 1,707 1,707 1,702 1,702 3,409 3,409 R2 1.39% 1.81% 2.19% 3.62% 0.77% 1.62%
142
Panel B. Market reaction to legislation related to risk oversight. Matched pairs
Cross–sectional regressions
on event days
Difference in coefficients on
event and non–event days Event #1 Event #2 Pooled Mean (t-test) Median (Wlx)
Intercept 2.59** 0.89 –3.14*** –5.12*** -0.31 –2.16** –1.00 –2.94 –0.94 –2.53
(2.26) (0.57) (–2.73) (–3.67) (-0.38) (–1.99) (–0.42) (–0.98) (–0.36) (–0.95)
NoRiskOversight 0.69*** 0.39** 0.55*** 0.58** 0.58** (3.48) (2.26) (4.11) (2.01) (2.00)
NoRiskCommittee 0.82 1.61*** 1.22*** 1.24* 1.26**
(1.60) (3.05) (3.25) (1.80) (2.02) NoCRO 0.61** 0.19 0.41** 0.44 0.38
(2.46) (0.70) (2.22) (1.25) (1.36)
NoERM 0.68* 0.44 0.57** 0.57 0.52*
(1.80) (1.29) (2.22) (1.41) (1.79)
NoRMstd 0.16 –0.06 0.05 0.08 0.08
(0.25) (–0.11) (0.11) (0.20) (0.13) NoOther 0.05 0.17 0.11 0.13 0.12
(0.22) (0.83) (0.73) (0.66) (0.95)
Staggered 0.02 0.04 0.39** 0.42** 0.21 0.23* 0.22 0.25 0.24 0.26 (0.12) (0.19) (2.16) (2.31) (1.52) (1.69) (1.43) (1.54) (1.20) (1.28)
ExcessPay 0.13 0.16 –0.08 –0.05 0.02 0.05 –0.01 0.02 0.00 0.03
(1.14) (1.38) (–0.94) (–0.61) (0.27) (0.75) (–0.08) (0.19) (–0.01) (0.34) NLargeInstit –0.40 –0.53* –0.06 –0.10 –0.23 –0.32 –0.25 –0.34 –0.29 –0.38
(–1.27) (–1.72) (–0.19) (–0.35) (–1.07) (–1.49) (–0.53) (–0.76) (–0.89) (–1.10)
NCoalitions 0.02 0.04 0.25** 0.25** 0.15* 0.16* 0.16 0.17 0.16 0.17 (0.13) (0.34) (2.16) (2.16) (1.73) (1.85) (1.42) (1.50) (1.40) (1.53)
IsChair –0.12 –0.13 –0.14 –0.12 –0.12 –0.12 –0.14 –0.13 –0.12 –0.11
(–0.54) (–0.58) (–0.72) (–0.65) (–0.81) (–0.80) (–0.66) (–0.65) (–1.08) (–1.06)
Size –0.22** –0.19** 0.16* 0.18** –0.03 0.00 0.03 0.06 0.03 0.06
(–2.42) (–1.98) (1.81) (2.14) (–0.52) (–0.03) (0.16) (0.31) (0.26) (0.34) BM 0.02 0.01 0.00 –0.01 0.01 0.00 0.00 0.00 –0.01 –0.02
(0.83) (0.47) (–0.33) (–1.18) (0.52) (–0.12) (0.06) (–0.05) (–0.28) (–0.56)
Momentum 0.89** 0.78* 0.61** 0.51** 0.56** 0.46** 1.32 1.21 0.84* 0.72* (2.17) (1.95) (2.18) (1.97) (2.31) (2.02) (0.73) (0.68) (1.92) (1.71)
N 1,008 1,008 1,000 1,000 2,008 2,008
R2 3.19% 4.34% 4.13% 6.77% 1.80% 3.53%
143
Table 6. Propensity-score Matched Pair Analysis
Panel A. Covariate balance
Panel A presents statistics of the covariate balance between 383 matched pairs from 2000 to 2006. The 385
control firms are those with ROindex>0 in the period 2000-2006. For each subsample, treatment and
control groups are formed using Derigs (1988) algorithm, which forms pairs by minimizing propensity
score differences and maximizing treatment differences. t-test p–values test for difference in means.
Wilcoxon Rank-sum p–values test for a difference in distributions. The variables are defined as in
appendix A.
Mean Median t-test Wilx
Trtmt Ctrl Trtmt Ctrl p-value p-value
Size 7.84 7.66 7.62 7.49 0.110 0.203
BM 0.54 0.63 0.49 0.45 0.201 0.149
Leverage 0.26 0.26 0.24 0.24 0.820 0.738
ROA 0.08 0.09 0.07 0.08 0.015 0.002
Return 0.21 0.22 0.16 0.19 0.638 0.126
IndustryVol 0.45 0.44 0.43 0.42 0.572 0.811
PctInstit 0.66 0.65 0.69 0.69 0.531 0.732
Cash 0.94 0.89 0.67 0.71 0.454 0.609
Delta 0.54 0.99 0.21 0.19 0.233 0.953
Vega 0.06 0.06 0.03 0.02 0.700 0.309
Age 53.97 53.57 53.69 53.85 0.426 0.908
144
Panel B. Difference in risk between matched pairs and sensitivity to hidden bias
This panel presents the difference in risk-related outcomes between the treatment (T) and control (C)
groups from 2000 to 2006. The propensity score is the conditional probability of receiving some level of
treatment given the observable covariates using the models in Table 2 (Panel A). ROindexT is the ROindex
of the observations in the treatment group. t-test p–values test for difference in means. Wilcoxon (Wlx)
Rank-sum p–values test for a difference in distribution. The variables are defined as in appendix A. Γ
values quantify the amount of hidden bias necessary to alter the statistical significance (p = 0.10) that
results from the assumption that two observations with identical propensity scores have an equal
probability of receiving treatment.
Outcome Mean Median t-test Wlx
Variable T C T C p-value p-value Γ
ROindexT > 0
(383 pairs)
Idvol 0.31 0.31 0.28 0.28 0.650 0.344
Beta 1.07 1.04 0.99 0.98 0.355 0.228
ExtremeRet 0.37 0.41 0.33 0.40 0.074 0.047 1.1
ExtremeROAdj 0.37 0.45 0.25 0.33 0.012 0.001 1.3
ExtremeROA 0.33 0.38 0.25 0.33 0.038 0.043 1.1
Rating 12.60 12.80 13.00 13.00 0.470 0.248
Allindrawn 112.07 124.59 82.87 104.17 0.107 0.030 1.2
ROindexT > 1
(133 pairs)
Idvol 0.27 0.29 0.24 0.27 0.108 0.016 1.2
Beta 0.97 1.04 0.88 0.96 0.152 0.091 1.2
ExtremeRet 0.28 0.39 0.25 0.33 0.004 0.006 1.3
ExtremeROAdj 0.21 0.42 0.00 0.27 0.000 0.000 2.0
ExtremeROA 0.25 0.34 0.14 0.23 0.032 0.027 1.2
Rating 13.57 13.38 14.00 13.50 0.660 0.193
Allindrawn 102.04 94.30 73.75 68.13 0.530 0.436
ROindexT > 2
(73 pairs)
Idvol 0.22 0.28 0.21 0.26 0.001 0.000 2.0
Beta 0.93 1.07 0.87 0.96 0.018 0.013 1.3
ExtremeRet 0.21 0.35 0.07 0.27 0.007 0.007 1.3
ExtremeROAdj 0.14 0.34 0.00 0.00 0.002 0.001 1.9
ExtremeROA 0.20 0.30 0.00 0.00 0.077 0.148
Rating 14.25 13.68 14.60 14.00 0.276 0.035 1.3
Allindrawn 86.09 78.25 53.08 63.00 0.654 0.252
ROindexT > 3
(55 pairs)
Idvol 0.22 0.28 0.21 0.28 0.003 0.001 1.8
Beta 0.95 1.09 0.87 1.02 0.054 0.023 1.3
ExtremeRet 0.21 0.33 0.14 0.25 0.043 0.062 1.1
ExtremeROAdj 0.13 0.31 0.00 0.00 0.012 0.008 1.6
ExtremeROA 0.18 0.32 0.00 0.14 0.032 0.108
Rating 14.37 13.70 14.55 13.50 0.255 0.049 1.2
Allindrawn 71.97 88.08 50.31 67.78 0.323 0.177
145
Table 7. Descriptive Statistics
Panel A: Distributional Statistics
Panel A presents descriptive statistics for our sample of 36,219 firm-years between 2002 and 2008. The
variables and their source are as defined in Appendix A. Delta, Vega, VPortf, and CashComp are expressed
in thousands of dollars.
Variable 25th
Pctle Median Mean 75th
Pctle Std Dev
Volatility 0.31 0.45 0.54 0.68 0.33
Idio Vol 0.28 0.41 0.49 0.62 0.32
Beta 0.50 0.90 0.96 1.33 0.64
Implied Vol 0.33 0.45 0.51 0.64 0.25
Extreme 0.00 0.00 0.20 0.00 0.40
R&D 0.00 0.04 0.10 0.12 0.24
AISD 62.50 125.00 153.16 225.00 119.26
Rating 9.00 12.00 11.86 14.00 3.40
RiskElasticity 0.04 0.09 0.12 0.17 0.13
PriceElasticity 0.54 0.63 0.68 0.76 0.21
VPortf 1,434 4,375 18,240 13,211 47,519
Vega 2.40 8.65 27.40 26.11 53.17
Delta 17.87 53.90 204.76 160.94 496.91
CashComp 266.75 384.20 530.67 608.80 460.58
Age 49.29 52.50 52.59 55.83 4.90
Size 4.98 6.12 6.22 7.39 1.86
BM 0.29 0.49 0.62 0.78 6.06
Leverage 0.02 0.17 0.22 0.34 0.26
ROA 0.02 0.09 0.05 0.15 0.29
Return -25.90 3.64 13.02 32.88 83.41
146
Panel B: Correlation Matrix
Panel B presents a correlation matrix of the primary variables in this study. Spearman rank order correlations are presented above the diagonal and Pearson
product moment correlations are presented below the diagonal. All of the variables are as defined in Appendix A
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)
(1) Volatility 0.98 0.24 0.95 0.34 0.43 0.51 -0.48 0.24 -0.48 -0.21 -0.27 -0.26 -0.31 -0.12 -0.45 0.01 -0.16 -0.24 -0.32
(2) Idio Vol 0.99 0.14 0.95 0.36 0.43 0.55 -0.53 0.22 -0.48 -0.25 -0.32 -0.30 -0.36 -0.13 -0.53 0.01 -0.17 -0.25 -0.29
(3) Beta 0.26 0.16 0.38 0.11 0.20 0.04 -0.26 0.08 -0.03 0.22 0.23 0.22 0.20 -0.13 0.32 -0.19 -0.09 0.01 -0.09
(4) Implied Vol 0.88 0.88 0.41 0.34 0.45 0.55 -0.52 0.23 -0.52 -0.26 -0.39 -0.33 -0.48 -0.16 -0.63 0.03 -0.20 -0.33 -0.34
(5) Extreme 0.34 0.35 0.13 0.35 0.18 0.24 -0.28 0.01 -0.19 -0.09 -0.16 -0.11 -0.12 -0.10 -0.19 -0.07 -0.05 -0.13 0.01
(6) R&D 0.31 0.32 0.04 0.38 0.14 0.00 0.04 0.24 -0.05 -0.18 -0.05 -0.18 -0.27 -0.12 -0.22 -0.28 -0.40 -0.44 -0.17
(7) AISD 0.47 0.50 0.05 0.52 0.26 0.20 -0.86 0.10 -0.29 -0.37 -0.49 -0.43 -0.44 -0.21 -0.67 0.16 0.17 -0.24 0.00
(8) Rating -0.40 -0.44 -0.27 -0.50 -0.28 -0.07 -0.75 -0.07 0.26 0.29 0.44 0.34 0.39 0.26 0.65 -0.05 -0.38 0.08 0.06
(9) RiskElast. 0.08 0.06 0.02 0.11 0.03 0.13 0.10 -0.06 0.54 -0.28 0.33 -0.24 -0.03 -0.09 -0.12 0.14 -0.06 -0.14 -0.32
(10) PriceElast. -0.41 -0.40 -0.07 -0.46 -0.17 -0.07 -0.25 0.26 0.43 0.00 0.52 0.08 0.23 0.00 0.25 0.01 0.01 0.09 0.07
(11) VPortf -0.09 -0.10 0.09 -0.10 -0.03 -0.07 -0.18 0.15 -0.14 -0.04 0.54 0.99 0.51 0.12 0.65 -0.31 0.04 0.34 0.26
(12) Vega -0.20 -0.23 0.08 -0.29 -0.12 -0.08 -0.36 0.44 0.07 0.32 0.33 0.61 0.57 0.06 0.67 -0.21 0.06 0.24 0.13
(13) Delta -0.11 -0.13 0.09 -0.14 -0.04 -0.07 -0.21 0.19 -0.14 0.00 0.99 0.40 0.54 0.12 0.69 -0.31 0.04 0.35 0.27
(14) CashComp -0.24 -0.26 0.08 -0.35 -0.11 -0.14 -0.31 0.35 -0.07 0.19 0.31 0.58 0.36 0.15 0.68 -0.10 0.22 0.33 0.13
(15) Age -0.12 -0.12 -0.14 -0.16 -0.11 -0.05 -0.19 0.26 -0.08 -0.01 0.09 0.10 0.09 0.14 0.10 0.08 0.09 0.10 0.05
(16) Size -0.43 -0.49 0.26 -0.58 -0.20 -0.21 -0.58 0.66 -0.13 0.27 0.36 0.61 0.41 0.59 0.11 -0.29 0.15 0.36 0.23
(17) BM -0.01 -0.02 -0.01 -0.02 -0.01 -0.01 -0.01 0.03 0.02 0.00 -0.01 -0.01 -0.01 0.00 0.01 -0.02 0.03 -0.20 -0.30
(18) Leverage 0.00 0.00 -0.05 -0.05 0.00 0.01 0.20 -0.35 -0.02 -0.01 0.00 0.03 0.01 0.10 0.02 0.05 -0.05 0.09 0.00
(19) ROA -0.33 -0.35 -0.02 -0.43 -0.15 -0.81 -0.23 0.12 -0.13 0.07 0.10 0.12 0.10 0.15 0.07 0.27 0.01 -0.04 0.23
(20) Return -0.05 -0.03 -0.04 -0.11 0.20 -0.06 0.10 -0.05 -0.21 -0.04 0.07 0.00 0.07 0.03 0.01 0.10 -0.02 -0.04 0.10
147
Table 8. Risk-taking Incentives and Equity Risk
Panel A: Future Return Volatility
Panel A presents the results of OLS regressions of future stock return volatility, Volatilityt+1, on incentive
variables and controls. Panel B presents the results of OLS regressions of fu ture id iosyncratic stock
return volatility, IdVolt+1
, on incentive variables and controls. Panel C presents the resu lts of OLS
regressions of fu ture systematic risk, Betat+1
, on incentive variables and controls. The variables are as
defined in Appendix A. t-statistics are reported in parentheses below the coefficient estimates and are calculated
based on two-way year and industry (two-digit SIC) clustered robust standard errors (Gow et al., 2009).
Statistical significance (two-sided) at the 1%, 5%, and 10% levels are denoted by ***, **, and *, respectively.
Volatilityt+1 Volatilityt+1 Volatilityt+1 Volatilityt+1 Volatilityt+1
Constant 1.006*** 1.437*** 1.301*** 1.495*** 0.628***
(10.42) (6.94) (7.96) (7.37) (3.86)
RiskElasticity 0.685*** 0.668*** 0.401**
(4.49) (4.30) (2.17)
PriceElasticity –0.565*** –0.588*** –0.203**
(–7.15) (–7.20) (–2.52)
VPortf 0.0004***
(3.00)
Vega 0.284* 0.576*** 0.055
(1.86) (2.98) (0.38)
Delta 0.057*** 0.036** 0.030***
(3.23) (2.55) (3.29)
CashComp 0.018 –0.009 –0.004 –0.001
(0.61) (–0.35) (–0.16) (–0.07)
Age –0.005* –0.005** –0.005** –0.002
(–1.93) (–2.00) (–2.02) (–1.19)
Size –0.072*** –0.056*** –0.081*** –0.062*** –0.030**
(–5.88) (–3.35) (–5.13) (–3.54) (–2.15)
BM –0.001 –0.001 –0.001 –0.001 –0.001
(–1.13) (–1.14) (–1.09) (–1.13) (–0.99)
Leverage 0.091* 0.087** 0.10** 0.089** 0.087***
(1.96) (2.05) (2.19) (2.12) (2.78)
ROA –0.259*** –0.223*** –0.252*** –0.218*** –0.090**
(–4.58) (–5.00) (–4.62) (–4.86) (–2.13)
Return –0.0004 –0.0004 –0.0004 –0.0004 –0.0004***
(–1.54) (–1.59) (–1.56) (–1.57) (–2.93)
Volatility 0.557***
(7.16)
Observations 36,219 36,219 36,219 36,219 36,219
Adj. R2
18.66% 25.57% 19.44% 25.87% 38.27%
148
Panel B: Future Idiosyncratic Volatility
IdVolt+1 IdVolt+1 IdVolt+1 IdVolt+1 IdVolt+1
Constant 1.023*** 1.423*** 1.325*** 1.494*** 0.655***
(10.60) (7.75) (8.77) (8.21) (4.29)
RiskElasticity 0.587*** 0.567*** 0.361**
(3.96) (3.74) (2.22)
PriceElasticity –0.478*** –0.506*** –0.176**
(–6.55) (–6.87) (–2.51)
VPortf 0.0004***
(3.48)
Vega 0.448*** 0.704*** 0.179
(3.51) (3.89) (1.35)
Delta 0.055*** 0.037*** 0.029***
(3.66) (3.06) (3.58)
CashComp 0.037 0.005 0.010 0.008
(1.38) (0.23) (0.47) (0.62)
Age –0.004** –0.005** –0.005** –0.002
(–2.22) (–2.32) (–2.36) (–1.43)
Size –0.083*** –0.074*** –0.097*** –0.081*** –0.042***
(–6.65) (–4.29) (–6.11) (–4.51) (–3.18)
BM –0.002 –0.002 –0.001 –0.002 –0.001
(–1.14) (–1.14) (–1.10) (–1.13) (–1.02)
Leverage 0.089** 0.082** 0.091** 0.085** 0.081***
(2.24) (2.30) (2.47) (2.39) (2.93)
ROA –0.259*** –0.227*** –0.250*** –0.222*** –0.095**
(–4.88) (–5.36) (–4.85) (–5.17) (–2.30)
Return –0.0004 –0.0004* –0.0004 –0.0004 –0.0004***
(–1.59) (–1.65) (–1.60) (–1.63) (–3.43)
Idio Vol 0.549***
(7.11)
Observations 36,219 36,219 36,219 36,219 36,219
Adj. R2
23.19% 28.65% 24.16% 29.12% 40.15%
149
Panel C: Future Systematic Risk (Beta)
Betat+1 Betat+1 Betat+1 Betat+1 Betat+1
Constant 0.418*** 1.318*** 0.942*** 1.17*** 0.245**
(5.34) (4.33) (3.68) (3.79) (2.06)
RiskElasticity 0.704*** 0.752*** 0.363***
(3.19) (3.25) (4.56)
PriceElasticity –0.729*** –0.677*** –0.288***
(–6.54) (–6.17) (–4.54)
VPortf 0.0001
(–0.47)
Vega –1.866*** –1.519*** –0.844***
(–4.41) (–5.07) (–4.29)
Delta 0.023 –0.001 0.002
(0.64) (–0.02) (0.10)
CashComp –0.066* –0.017 –0.011 0.025
(–1.95) (–0.38) (–0.28) (0.84)
Age –0.014*** –0.013*** –0.013*** –0.001
(–2.67) (–2.71) (–2.59) (–0.37)
Size 0.097*** 0.137*** 0.133*** 0.154*** 0.057***
(10.41) (12.28) (12.62) (14.28) (4.45)
BM –0.000 0.000 0.000 0.000 0.000
(–0.13) (0.18) (0.19) (0.15) (0.43)
Leverage –0.057 –0.052 –0.050 –0.058 0.046
(–0.52) (–0.55) (–0.51) (–0.62) (1.04)
ROA –0.127 –0.084 –0.132* –0.095 0.014
(–1.60) (–1.38) (–1.90) (–1.57) (0.40)
Return 0.000 0.001 0.000 0.000 0.001*
(0.76) (0.95) (0.61) (0.87) (1.95)
Betat 0.605***
(9.40)
Observations 36,219 36,219 36,219 36,219 36,219
Adj. R2
8.09% 13.67% 10.81% 14.51% 45.94%
150
Table 9. Risk-taking Incentives and Credit Risk
Panel A: Credit Ratings (Ordered Logit)
Panel A presents the results of ordered logit regressions of future credit ratings, Ratingt+1, on incentive
variables and controls. Panel B presents the results of OLS regressions of future all-in drawn spreads,
Allindrawnt+1, on incentive variables and controls. The variables are as defined in Appendix A. t-statistics
are reported in parentheses below the coefficient estimates and are calculated based on two-way year and
firm clustered robust standard errors (Gow et al., 2009). Statistical significance (two-sided) at the 1%, 5%,
and 10% levels are denoted by ***, **, and *, respectively.
Ratingt+1 Ratingt+1 Ratingt+1 Ratingt+1 Ratingt+1
RiskElasticity –1.166* –1.397** –1.519**
(–1.73) (–2.24) (–2.38)
PriceElasticity 0.024 –0.323 –0.358
(0.07) (–1.10) (–1.49)
VPortf 0.0003
(0.49)
Vega 3.623*** 4.650*** 1.808***
(5.82) (7.26) (2.82)
Delta 0.002 –0.066 0.084*
(0.03) (–0.94) (1.65)
CashComp –0.044 –0.162* –0.201** 0.098**
(–0.49) (–1.83) (–2.24) (2.27)
Age 0.064*** 0.065*** 0.063*** –0.005
(6.32) (6.19) (6.18) (–0.70)
LogTA 0.938*** 0.929*** 0.865*** 0.868*** 0.113***
(27.10) (23.41) (20.48) (19.50) (2.57)
BM 0.002 0.003 0.006 0.007 0.003*
(0.11) (0.24) (0.50) (0.73) (1.95)
Leverage –2.954*** –2.878*** –2.834*** –2.847*** –1.295***
(–13.50) (–13.42) (–12.97) (–13.12) (–7.22)
ROA 6.765*** 6.793*** 6.358*** 6.346*** 4.023***
(8.81) (9.72) (9.01) (9.53) (8.56)
Idio Vol –3.161*** –3.279*** –3.349*** –3.425*** –2.588***
(–5.58) (–6.55) (–6.81) (–6.98) (–5.37)
Beta –0.917*** –0.834*** –0.840*** –0.838*** –0.136**
(–6.10) (–6.82) (–6.30) (–6.94) (–2.03)
Return –0.001 –0.002** –0.001 –0.002** 0.006***
(–1.13) (–2.32) (–1.09) (–2.13) (6.53)
Ratingt 2.886****
(32.59)
Observations 11,919 11,919 11,919 11,919 11,464
Adj. R2
18.43% 19.04% 19.21% 19.44% 61.95%
151
Panel B: All-in-drawn Spread Allindrawnt+1 Allindrawnt+1 Allindrawnt+1 Allindrawnt+1 Allindrawnt+1
Constant 137.552*** 182.297*** 158.493*** 168.350*** 65.034**
(7.43) (8.12) (7.44) (7.62) (2.49)
RiskElasticity 160.479*** 169.020*** 128.707***
(6.50) (7.04) (3.64)
PriceElasticity –39.695*** –32.087*** –21.230**
(–3.60) (–2.82) (–2.17)
VPortf –0.046*
(–1.83)
Vega –86.625*** –131.538*** –104.254**
(–4.51) (–6.27) (–2.25)
Delta –5.898** –2.054 1.111
(–2.40) (–0.84) (0.26)
CashComp –4.754 –1.958 0.456 –2.775
(–1.54) (–0.85) (0.20) (–0.78)
Age –0.708** –0.608** –0.693** –0.100
(–2.45) (–2.30) (–2.48) (–0.37)
LogTA –12.306*** –10.310*** –9.572*** –9.134*** –3.330
(–6.40) (–5.21) (–4.25) (–4.55) (–1.45)
BM 3.134*** 2.240* 2.750** 1.935 0.237
(2.74) (1.84) (2.51) (1.60) (0.04)
Leverage 100.546*** 96.502*** 95.475*** 93.62*** 32.737**
(8.23) (8.22) (8.27) (7.86) (2.50
ROA –119.805*** –115.553*** –114.381*** –112.699*** –80.446*
(–3.96) (–3.97) (–3.79) (–3.92) (–1.87)
Idio Vol 129.665*** 120.005*** 131.788*** 123.500*** 114.473***
(5.94) (6.22) (6.07) (6.27) (4.09)
Beta –8.591 –10.257** –9.178* –10.626** –12.892***
(–1.62) (–2.02) (–1.82) (–2.10) (–2.81)
Return –0.083*** –0.055** –0.081*** –0.056** –0.156***
(–3.03) (–2.36) (–2.98) (–2.42) (–5.70)
DealAmount 0.002 0.003* 0.003* 0.004** 0.004**
(0.93) (1.78) (1.67) (2.35) (2.32)
Secured 93.203*** 88.040*** 91.654*** 87.387*** 64.212***
(18.19) (15.86) (17.91) (16.35) (8.25)
Maturity 0.108 0.181* 0.088 0.158 0.201
(1.13) (1.91) (0.91) (1.62) (1.48)
Allindrawnt 0.365***
(9.34)
Observations 4,631 4,631 4,631 4,631 1,931
Adj. R2 49.88% 50.94% 50.14% 51.14% 62.92%
152
Table 10. Alternative Measures of Risk-taking Behavior
Panel A: Extreme Outcomes
This table presents the results of logit regressions of future extreme returns (Extremet+1) on equity incentive variables
and controls. Panel B presents the results of OLS regressions of future implied volatility (Implied Volatilityt+1) on
equity incentive variables and controls. Panel C presents the results of tobit regressions of future research and
development expenses (R&Dt+1) on equity incentive variables and controls. The variables are as defined in Appendix
A. t-statistics are reported in parentheses below the coefficient estimates and are calculated based on two-way year and
firm clustered robust standard errors (Gow et al., 2009). Statistical significance (two-sided) at the 1%, 5%, and 10%
levels are denoted by ***, **, and *, respectively.
Extremet+1 Extremet+1 Extremet+1 Extremet+1 Extremet+1
Constant –1.015*** 0.966*** 0.609** 0.876*** 0.719***
(–4.61) (4.40) (2.26) (3.72) (3.38)
RiskElasticity 1.033** 1.051** 0.970**
(2.15) (2.17) (2.18)
PriceElasticity –0.672*** –0.637*** –0.586***
(–3.46) (–3.25) (–3.15)
VPortf 0.002**
(2.46)
Vega –1.243** –1.201** –1.152**
(–2.05) (–2.10) (–2.19)
Delta 0.186*** 0.192*** 0.188***
(2.59) (2.65) (2.60)
CashComp –0.016 0.011 0.013 0.003
(–0.21) (0.14) (0.17) (0.04)
Age –0.030*** –0.030*** –0.030*** –0.028***
(–4.98) (–4.95) (–4.95) (–4.78)
Size –0.196*** –0.197*** –0.199*** –0.188*** –0.182***
(–7.96) (–5.76) (–6.81) (–5.38) (–5.46)
BM 0.002 0.002 0.002 0.002 0.002
(0.67) (0.73) (0.76) (0.74) (0.78)
Leverage 0.208 0.23*0 0.232* 0.227* 0.215*
(1.59) (1.81) (1.69) (1.78) (1.70)
ROA –0.441*** –0.395*** –0.431*** –0.397*** –0.354***
(–3.64) (–3.63) (–3.60) (–3.64) (–3.28)
Vol 1.274*** 1.085*** 1.218*** 1.097*** 0.965***
(5.54) (5.42) (5.68) (5.53) (4.59)
Return 0.001 0.001* 0.001 0.001* 0.000
(1.37) (1.75) (1.31) (1.70) (1.07)
Extremet 0.378***
(4.26)
Observations 36,219 36,219 36,219 36,219 36,219
Adj. R2 8.13% 8.73% 8.52% 8.75% 9.06%
153
Panel B: Implied Volatility
Implied
Volatilityt+1
Implied
Volatilityt+1
Implied
Volatilityt+1
Implied
Volatilityt+1
Implied
Volatilityt+1
Constant 1.026*** 1.231*** 1.128*** 1.287*** 0.353***
(24.81) (8.85) (12.76) (9.53) (3.29)
RiskElasticity 0.415*** 0.395*** 0.188**
(4.77) (4.69) (2.19)
PriceElasticity –0.421*** –0.437*** –0.119***
(–7.01) (–6.97) (–3.02)
VPortf 0.0003**
(2.33)
Vega 0.109 0.349** –0.101
(0.78) (2.57) (–1.16)
Delta 0.043*** 0.022** 0.013***
(2.72) (1.98) (2.88)
CashComp –0.033** –0.052*** –0.045*** –0.021
(–2.02) (–3.20) (–3.11) (–1.50)
Age –0.003 –0.002 –0.003 –0.001
(–1.45) (–1.11) (–1.50) (–1.01)
Size –0.067*** –0.041*** –0.065*** –0.048*** –0.006
(–13.18) (–5.01) (–7.68) (–5.29) (–0.63)
BM –0.001 0.000 0.001 0.000 0.002***
(–0.19) (0.03) (0.15) (0.11) (4.75)
Leverage –0.012 –0.006 0.003 –0.002 0.048***
(–0.30) (–0.19) (0.08) (–0.08) (3.16)
ROA –0.351*** –0.334*** –0.349*** –0.327*** –0.14***
(–8.09) (–9.3) (–8.44) (–9.09) (–4.94)
Return –0.000 –0.000 –0.000 –0.000 –0.000**
(–0.82) (–0.84) (–0.89) (–0.80) (–2.01)
Implied Volt-1 0.667***
(9.11)
Observations 20,339 20,339 20,339 20,339 18,523
Adj. R2
33.89% 45.55% 35.57% 46.01% 68.20%
154
Panel C: Future R&D Expenditures
R&Dt+1 R&Dt+1 R&Dt+1 R&Dt+1 R&Dt+1
Constant –0.278*** –0.367*** –0.197** –0.288** 0.044
(–5.14) (–3.21) (–1.97) (–2.36) (1.10)
RiskElasticity 0.384*** 0.370*** 0.106**
(4.00) (3.89) (2.53)
PriceElasticity 0.006 –0.025 –0.024**
(0.17) (–0.78) (–2.51)
VPortf –0.000**
(–2.05)
Vega 0.89*** 0.675*** 0.042
(4.05) (3.36) (1.05)
Delta –0.038*** –0.023*** 0.001
(–3.52) (–3.27) (0.60)
CashComp –0.068*** –0.103*** –0.097*** –0.009***
(–3.46) (–4.38) (–3.94) (–3.49)
Age 0.016*** –0.000 –0.001* –0.001 –0.000
(3.14) (–0.63) (–1.76) (–0.86) (–0.66)
Size –0.001 0.029** 0.017*** 0.02 0.000
(–1.48) (2.18) (2.68) (0.10) (0.16)
bm –0.257*** –0.001*** –0.001*** –0.001*** 0.000
(–5.76) (–4.35) (–3.99) (–4.44) (–1.23)
Leverage –0.397*** –0.243*** –0.243*** –0.240*** –0.042***
(–6.09) (–5.61) (–5.62) (–12.72) (–7.10)
ROA 0.000 –0.379*** –0.391*** –0.377*** –0.071**
(0.19) (–6.84) (–6.02) (–6.77) (–2.03)
Return 0.194*** 0.000 0.000 0.000 0.000
(3.90) (0.02) (0.01) (0.02) (1.07)
Volatilityt 0.203*** 0.190*** 0.192*** 0.016
(3.76) (3.85) (3.51) (1.07)
R&Dt 0.484***
(6.87)
Observations 36,219 36,219 36,219 36,219 36,219
Adj. R2
18.58% 20.97% 19.89% 21.41% 28.13%
155
Table 11. Propensity Score Matched Pair Analysis
Panel A: Matching on RiskElasticity
Panel A presents results of propensity score matching analysis using RiskElasticity as experimental
variable. Panel A shows statistics of differences of covariates, RiskElasticity and dependent variables
between 17,200 matched pairs (5% of the pairs are eliminated to improve covariance balance). Treatment
(Treat) and control (Ctrl) groups are formed using Derigs (1988) optimal algorithm, which forms pairs by
minimizing propensity score differences and maximizing treatment (RiskElasticity) differences. t-statistics
correspond to parametric tests for the difference in means and medians and are computed using two-way
clustered standard errors (Gow et al., 2009). Γ values quantify the amount of hidden bias necessary to alter
the statistical significance (p = 0.10) that results from the assumption that two observations with identical
propensity scores have an equal probability of receiving treatment. Γ are calculated for the dependent
variables when the p-value from the Wilcoxon test is less than 0.10. The variables are defined as in
appendix A. Statistical significance (two-sided) at the 1%, 5%, and 10% levels are denoted by ***, **, and
*, respectively.
Mean Median
Treat Ctrl t-stat Treat Ctrl t-stat Γ
Volatilityt+1 0.547 0.486 2.24** 0.488 0.392 3.23*** 1.7
Idio Volt+1 0.492 0.437 1.98** 0.437 0.349 3.26*** 1.6
Betat+1 1.088 0.920 3.50*** 1.047 0.867 4.38*** 1.7
Ratingt+1 11.353 12.230 –1.96** 11.000 13.000 –1.93* 1.4
AISDt+1 165.078 139.498 1.59 137.500 110.000 1.50 1.1
Extremet+1 0.211 0.165 1.76* 0.000 0.000 n.a. 1.4
Implied Volt+1 0.522 0.466 1.72* 0.484 0.389 2.61*** 1.6
RDt+1 0.062 0.036 2.73*** 0.000 0.000 n.a. 1.8
RiskElasticityt 0.181 0.056 6.96*** 0.145 0.042 5.60***
PriceElasticityt 0.704 0.658 2.75*** 0.659 0.592 5.14***
VPortft 17.797 19.506 –1.11 4.206 4.994 –1.72*
CashCompt 0.551 0.523 0.71 0.402 0.374 1.24
Aget 52.447 52.773 –1.25 52.400 52.750 –1.13
Sizet 6.357 6.224 0.63 6.229 6.108 0.62
BMt 0.602 0.676 –1.13 0.479 0.497 –1.68*
Leveraget 0.218 0.221 –0.33 0.166 0.168 –0.13
ROAt 0.055 0.063 –0.53 0.092 0.085 1.19
Returnt 15.550 15.164 0.09 –0.497 9.537 –4.04***
156
Panel B: Matching on Vega
Panel B presents results of propensity score matching analysis using Vega as experimental variable. Panel
B shows statistics of differences of covariates, Vega and dependent variables between 17,200 matched pairs
(5% of the pairs are eliminated to improve covariance balance). Treatment (Treat) and control (Ctrl) groups
are formed using Derigs (1988) optimal algorithm, which forms pairs by minimizing propensity score
differences and maximizing treatment (Vega) differences. t-statistics correspond to parametric tests for the
difference in means and medians and are computed using two-way clustered standard errors (Gow et al.,
2009). Γ values quantify the amount of hidden bias necessary to alter the statistical significance (p = 0.10)
that results from the assumption that two observations with identical propensity scores have an equal
probability of receiving treatment. Γ are calculated for the dependent variables when the p-value from the
Wilcoxon test is less than 0.10. The variables are defined as in appendix A. Statistical significance (two-
sided) at the 1%, 5%, and 10% levels are denoted by ***, **, and *, respectively.
Mean
Median
Treat Ctrl t-stat Treat Ctrl t-stat Γ
Volatilityt+1 0.527 0.587 –2.27** 0.454 0.474 –0.93 1.3
Idio Volt+1 0.475 0.534 –2.23** 0.403 0.423 –1.17 1.4
Betat+1 0.998 1.018 –0.97 0.951 0.963 –0.70 1.1
Ratingt+1 11.969 10.951 6.21*** 12.000 11.000 3.24*** 1.8
AISDt+1 145.801 175.863 –4.03*** 112.500 150.000 –4.18*** 1.6
Extremet+1 0.191 0.212 –1.90* 0.000 0.000 n.a. 1.2
Implied Volt+1 0.495 0.537 –2.48** 0.451 0.481 –2.19** 1.6
RDt+1 0.064 0.042 3.06*** 0.000 0.000 n.a. 1.6
RiskElasticityt 0.042 0.007 7.07*** 0.018 0.004 6.11***
PriceElasticityt 0.222 0.159 8.58*** 0.070 0.040 8.44***
VPortft 18.996 15.111 2.81*** 5.384 3.353 5.84***
CashCompt 0.568 0.452 6.14*** 0.413 0.348 5.57***
Aget 52.971 52.120 4.42*** 53.000 52.000 4.39***
Sizet 6.413 5.932 5.88*** 6.154 6.012 2.57***
BMt 0.582 0.747 –2.06** 0.477 0.516 –2.66***
Leveraget 0.219 0.222 –0.22 0.171 0.162 0.63
ROAt 0.051 0.047 0.31 0.092 0.080 2.78***
Returnt 10.889 15.840 –1.71* 1.477 5.787 –1.89*
157
Table 12. Robustness to Model Specification and Functional Form
Panel A: Ranked Independent Variables
Panel A presents the results of OLS regressions of Volatilityt+1 (columns one and two) and R&Dt+1
(columns three and four) on fractional ranks of the independent variables. The variables are as defined in
Appendix A. t-statistics are reported in parentheses below the coefficient estimates and are calculated based
on two-way year and firm clustered robust standard errors (Gow et al., 2009). Statistical significance (two-
sided) at the 1%, 5%, and 10% levels are denoted by ***, **, and *, respectively.
Volatilityt+1 Volatilityt+1 R&Dt+1 R&Dt+1
Constant 1.161*** 1.227*** 0.234*** 0.255***
(8.81) (10.46) (10.22) (8.71)
RiskElasticity 0.286*** 0.047***
(4.14) (4.62)
PriceElasticity –0.495*** 0.005
(–9.99) (0.56)
Vportf –0.011 –0.015**
(–0.23) (–2.32)
Vega 0.057 –0.043***
(1.03) (–4.36)
Delta –0.170*** 0.059***
(–2.72) (8.01)
CashComp 0.076 0.082 0.038*** 0.034***
(1.51) (1.47) (3.68) (3.09)
Age –0.047 –0.049 0.015** 0.013**
(–1.44) (–1.49) (2.26) (2.20)
Size –0.323*** –0.394*** –0.056*** –0.074***
(–3.80) (–5.57) (–5.08) (–6.08)
BM –0.217*** –0.254*** –0.183*** –0.180***
(–5.72) (–7.12) (–9.27) (–9.08)
Leverage 0.052 0.050 –0.068*** –0.069***
(1.30) (1.24) (–9.27) (–8.87)
ROA –0.202*** –0.225*** –0.162*** –0.161***
(–4.62) (–4.87) (–11.05) (–10.68)
Return –0.323*** –0.433*** –0.040*** –0.048***
(–4.90) (–5.98) (–9.00) (–7.81)
Volatility 0.060*** 0.065***
(8.23) (7.62)
Observations 36,219 36,219 36,219 36,219
Adj. R2 30.73% 24.77% 14.44% 14.33%
158
Panel B: Additional Robustness Checks
Panel B presents the results of modifying the specification of OLS regressions of return volatility (Volatilityt+1) on
equity incentive variables and controls. The first two columns present results of modifying the initial specification by
using a logarithmic transformation of Volatilityt+1 as dependent variable. The third and fourth columns present results
of modifying the initial specification by including the median return volatility of all firms within the same two-digit
SIC code (Industry Vol) as additional control. The fifth and sixth columns present results of modifying the initial
specification by using logarithm of total assets as an alternative proxy for firm size. The variables are as defined in
Appendix A. t-statistics are reported in parentheses below the coefficient estimates and are calculated based on two-
way year and firm clustered robust standard errors (Gow et al., 2009). Statistical significance (two-sided) at the 1%,
5%, and 10% levels are denoted by ***, **, and *, respectively.
Log(Volatilityt+1) Log(Volatilityt+1) Volatilityt+1 Volatilityt+1 Volatilityt+1 Volatilityt+1
Constant 0.842*** 0.541*** 1.110*** 0.950*** 1.311*** 1.082***
(3.00) (2.65) (5.74) (5.82) (6.51) (6.66)
RiskElasticity 1.423*** 0.446* 0.736***
(4.98) (1.89) (5.31)
PriceElasticity –1.156*** –0.358*** –0.61***
(–6.69) (–3.88) (–7.06)
VPortf 0.001*** 0.0004*** 0.0002
(2.75) (3.27) (0.86)
Vega 0.209 0.014 –0.224
(0.63) (0.14) (–0.82)
Delta 0.089*** 0.043*** 0.028
(3.11) (4.05) (1.37)
CashComp –0.038 –0.079* 0.026 0.017 –0.010 –0.024
(–0.81) (–1.82) (0.79) (0.60) (–0.46) (–1.33)
Age –0.009** –0.010** –0.005*** –0.006*** –0.004 –0.003
(–2.57) (–2.51) (–2.62) (–2.87) (–1.50) (–1.27)
Size –0.077*** –0.122*** –0.058*** –0.071***
(–3.89) (–5.74) (–3.42) (–4.76)
LogTA –0.038*** –0.054***
(–4.82) (–6.58)
BM –0.001 –0.001 –0.001 –0.001 –0.001 0.000
(–1.07) (–0.92) (–1.12) (–1.08) (–0.99) (–0.61)
Leverage 0.005 0.020 0.123*** 0.136*** 0.132*** 0.158***
(0.07) (0.32) (5.16) (5.59) (3.87) (5.37)
ROA –0.252*** –0.315*** –0.207*** –0.220*** –0.224*** –0.258***
(–4.67) (–4.33) (–5.04) (–4.37) (–6.04) (–5.96)
Return 0.000 –0.001 0.000 0.000 –0.001* –0.001*
(–0.80) (–1.07) (–1.53) (–1.46) (–1.83) (–1.87)
Industry Vol 0.513*** 0.641***
(3.33) (4.95)
Observations 36,219 36,219 36,219 36,219 36,219 36,219
Adj. R2 38.06% 24.27% 30.47% 28.31% 24.01% 16.68%
159
Table 13. Variations in the calculation of RiskElasticity
This table presents the results of regressing future stock volatility (Volatilityt+1) on variations of the
RiskElasticity measure. The first column present benchmark results with the unmodified definition of
RiskElasticity. The second column presents results calculating RiskElasticity restricting (p,) pairs to those
such that 0 ≤ abs(p - ≤50%. p and are changes in stock price (p) and return volatility () with
respect to the values of p and in that fiscal year. The third column presents results calculating
RiskElasticity restricting (p,) pairs to those such that 0 ≤ p ≤50% and 0≤ ≤50%. The fourth column
presents results calculating RiskElasticity including (p,) pairs such that p < 0 and < 0. The fifth
column presents results using Vega scaled by portfolio value as measure of risk incentives. The sixth
column presents results calculating RiskElasticity without including the cross-derivative of portfolio value
with respect to p and . The variables are as defined in Appendix A. t-statistics are reported in parentheses
below the coefficient estimates and are calculated based on two-way year and firm clustered robust
standard errors (Gow et al., 2009). Statistical significance (two-sided) at the 1%, 5%, and 10% levels are
denoted by ***, **, and *, respectively.
p≥0 and
≥0
0≤abs(p-
≤50%
0≤p≤50%
and
0≤≤50%
Including
p<0 and
<0
Delta/VPortf
and
Vega/VPortf
RiskElasticity
without cross-
derivative
Constantt 1.437*** 1.452*** 1.436*** 1.438*** 1.681*** 1.458***
(6.94) (6.96) (6.92) (7.00) (8.53) (7.10)
Risk Incentive Measure 0.685*** 4.406*** 0.834*** 0.561*** 0.123*** 0.870***
(4.49) (4.73) (4.51) (3.93) (2.68) (4.34)
Return Incentive Measure –0.565*** –3.843*** –0.708*** –0.441*** –0.435*** –0.607***
(–7.15) (–7.44) (–7.10) (–7.12) (–7.45) (–7.26)
VPortft 0.0004*** 0.0004*** 0.0004*** 0.0004*** 0.0004*** 0.0004***
(3.00) (3.02) (2.98) (2.93) (2.63) (3.14)
CashCompt 0.018 0.019 0.018 0.019 0.024 0.018
(0.61) (0.63) (0.61) (0.62) (0.82) (0.57)
Aget –0.005* –0.005* –0.005* –0.005* –0.005** –0.005*
(–1.93) (–1.91) (–1.94) (–1.94) (–2.14) (–1.90)
Sizet –0.056*** –0.055*** –0.056*** –0.055*** –0.060*** –0.057***
(–3.35) (–3.21) (–3.33) (–3.28) (–3.75) (–3.45)
Book-to-Mkt –0.001 –0.001 –0.001 –0.001 –0.001 –0.001
(–1.14) (–1.15) (–1.14) (–1.14) (–1.14) (–1.12)
Leveraget 0.087** 0.086** 0.087** 0.086** 0.077* 0.090**
(2.05) (2.02) (2.05) (2.04) (1.75) (2.12)
ROAt –0.223*** –0.218*** –0.222*** –0.219*** –0.240*** –0.226***
(–5.00) (–4.96) (–5.01) (–4.99) (–4.86) (–4.88)
Returnt –0.000 –0.000 –0.000 –0.000 –0.000* –0.000
(–1.59) (–1.55) (–1.59) (–1.58) (–1.70) (–1.63)
Observations 36,219 36,219 36,219 36,219 36,219 36,219
Adj. R2 25.57% 26.10% 25.63% 26.00% 23.99% 25.01%
160
Table 14. Descriptive Statistics
This table presents descriptive statistics for firms in our sample. Panel A reports the industry distribution
of sample observations, classified by Fama and French (1997) industry groups. Panels A also report the
industry distribution of firms in the intersection between CRSP and Compustat. Panel B reports descriptive
statistics for the main variables used in the statistical tests. Panel C reports the correlation matrix for the
variables of the analysis. See Appendix B for variable definitions.
Panel A. Industry Classification
Fama–French Industry Group
% of Sample
5,207 firms
% of CRSP/Compustat
10,867 firms
Computers & Business Equipment 18.76% 17.99%
Chemicals and Allied Products 2.49% 1.55%
Consumer Durables 2.27% 1.8%
Energy 5.28% 3.43%
Healthcare 13.75% 9.09%
Manufacturing 9.49% 7.08%
Finance 17.04% 31.25%
Consumer Non–durables 4.54% 3.87%
Wholesale, Retail, Laundries, Repair Shops 9.09% 7.1%
Telephone and Television Transmission 2.82% 3.56%
Utilities 2.73% 1.62%
Other 11.73% 11.65%
Panel B. Distributional Statistics
Variable 25th Median Mean 75th Stdv
R&D 0.007 0.045 0.110 0.119 0.237
Idvol 0.267 0.355 0.401 0.479 0.209
PctDED 0.000 0.000 0.020 0.003 0.050
PctACT 0.003 0.009 0.013 0.022 0.013
PctLT 0.000 0.210 0.265 0.492 0.258
ReturnIncentive 0.0103 0.0117 0.0125 0.0140 0.0027
RiskIncentive 0.0003 0.0023 0.0044 0.0065 0.0055
VPortf 2.61 9.03 38.12 29.58 94.14
CashComp 0.38 0.55 0.71 0.85 0.59
Age 50.00 55.00 55.01 60.00 7.71
Tenure 2.50 5.70 7.52 10.10 6.74
Size 5.05 6.17 6.32 7.45 1.84
BM 0.26 0.47 0.56 0.74 1.26
Leverage 0.02 0.15 0.21 0.32 0.24
ROA 0.02 0.09 0.05 0.15 0.23
Beta 0.59 0.98 0.94 1.29 0.50
IndustryVol 0.36 0.41 0.40 0.44 0.07
161
Table 15. Shareholder Monitoring and the Effect of Risk–Taking Incentives
Panel A reports results for estimating research and development (R&D) as a function of the interaction between RiskIncentive and three proxies for shareholder
monitoring (ShrMonit): pctDED, pctACT and pctLT (see Appendix B for variable definitions). Panel B shows the results of similar regressions using
idiosyncratic equity risk as an alternative proxy for risk-taking behavior. See Appendix B for variable definitions. t-statistics are based on standard errors
clustered by firm and year to correct for time-series and cross-sectional dependence respectively. ***, **, and * denote statistical significance at the 0.01, 0.05,
and 0.10 levels (two-tail) respectively.
Panel A. R&D investment (Tobit regressions)
Proxy for ShrMonit pctDED pctACT pctLT
Dependent variable R&Dt+1
R&Dt+1
R&Dt+1
R&Dt+1
R&Dt+1
R&Dt+1
Independent variables coef t-stat coef t-stat coef t-stat coef t-stat coef t-stat coef t-stat
Constant 0.03 1.50 0.03 1.43 0.02 1.32 0.00 0.20 0.00 0.11 –0.02 –1.34
ShrMonit*RiskIncentive –16.81*** –3.02 –196.00*** –4.73 –9.89*** –3.67
ShrMonit –0.17*** –4.35 –0.08* –1.93 –0.55** –2.01 0.28 1.38 –0.08*** –8.15 –0.03*** –2.86
RiskIncentive 7.05*** 3.07 7.90*** 3.59 6.80*** 2.84 10.17*** 3.62 6.74*** 2.93 9.95*** 3.55
ReturnIncentive –4.97 –1.45 –5.08 –1.52 –4.27 –1.21 –3.80 –1.14 –3.45 –1.02 –2.57 –0.82
VPortf –0.00 –0.75 –0.00 –0.81 –0.00 –1.00 –0.00 –1.21 –0.00002 –1.56 –0.00003* –1.88
CashComp –0.01*** –5.09 –0.01*** –4.93 –0.01*** –5.27 –0.01*** –4.98 –0.01*** –5.22 –0.01*** –5.20
Age –0.001*** –2.88 –0.001*** –2.88 –0.001*** –3.10 –0.001*** –3.21 –0.001** –2.49 –0.001*** –2.74
Tenure 0.001*** 4.10 0.001*** 4.16 0.001*** 4.50 0.001*** 4.62 0.001*** 5.00 0.001*** 5.16
Size 0.01*** 9.80 0.01*** 9.74 0.01*** 10.70 0.01*** 10.85 0.02*** 11.85 0.02*** 12.00
BM –0.002*** –2.58 –0.002*** –2.58 –0.002** –2.52 –0.002** –2.49 –0.002** –2.50 –0.002** –2.46
Leverage –0.11*** –8.27 –0.11*** –8.29 –0.12*** –8.62 –0.12*** –8.79 –0.11*** –6.33 –0.11*** –8.04
ROA –0.51*** –7.63 –0.51*** –7.62 –0.51*** –7.69 –0.51*** –7.75 –0.50*** –7.64 –0.50*** –7.70
CAPEX –0.51*** –3.56 –0.51*** –3.54 –0.51*** –3.59 –0.51*** –8.79 –0.51*** –3.54 –0.51*** –3.56
Volatility 0.00 0.59 0.00 0.61 0.01 0.75 0.01 1.34 –0.00 –0.34 0.00 0.51
IndustryVol 0.18*** 3.84 0.18*** 17.07 0.17*** 3.63 0.16*** 3.61 0.17*** 3.87 0.17*** 3.84
N 12,792 12,792 12,792 12,792 12,792 12,792
Adj R2 67.01% 67.62% 67.17% 67.26% 67.46% 67.88%
162
Panel B. Idiosyncratic Return Volatility (OLS regressions)
Proxy for ShrMonit pctDED pctACT pctLT
Dependent variable Log(Idvolt+1) Log(Idvolt+1) Log(Idvolt+1) Log(Idvolt+1) Log(Idvolt+1) Log(Idvolt+1)
Independent variables coef t–stat coef t–stat coef t–stat coef t–stat coef t–stat coef t–stat
Constant –0.14 –0.45 –0.15 –0.47 –0.14 –0.46 –0.18 –0.56 –0.20 –0.69 –0.23 –0.76
ShrMonit*RiskIncentive –39.37** –2.16 –319.00*** –4.58 –10.09*** –2.68
ShrMonit –0.58* –1.82 –0.40 –1.37 –1.35* –1.80 –0.03 –0.05 –0.20*** –2.80 –0.16** –2.10
RiskIncentive 22.84** 2.16 24.80** 2.43 21.97** 2.03 27.17** 2.47 21.81** 2.06 24.93*** 2.57
ReturnIncentive –53.08*** –2.91 –53.19*** –2.97 –51.21*** –2.81 –50.51*** –2.83 –48.95*** –2.80 –48.11*** –2.76
VPortf –0.00 –0.35 –0.00 –0.43 –0.00 –0.59 –0.00 –0.72 –0.00 –1.63 –0.000003* –1.83
Cash –0.03 –1.34 –0.03 –1.33 –0.03 –1.31 –0.03 –1.30 –0.03 –1.27 –0.03 –1.28
Age –0.004*** –4.72 –0.004*** –4.70 –0.004*** –4.42 –0.004*** –4.38 –0.004*** –4.40 –0.004*** –4.39
Tenure –0.00 –0.22 –0.00 –0.21 0.00 0.24 0.00 0.33 0.00 0.83 0.00 0.85
Size –0.07*** –5.81 –0.07*** –5.89 –0.07*** –5.37 –0.07*** –5.41 –0.06*** –4.36 –0.06*** –4.33
BM –0.003** –2.16 –0.003** –2.20 –0.003** –2.28 –0.003** –2.26 –0.003** –2.01 –0.003** –2.02
Leverage 0.07 1.47 0.07 1.49 0.06 1.29 0.06 1.30 0.07 1.46 0.07 1.48
ROA –0.15*** –5.22 –0.15*** –5.22 –0.15*** –5.09 –0.15*** –5.22 –0.14*** –4.99 –0.14*** –5.05
Volatility 0.71*** 5.52 0.71*** 5.56 0.71*** 5.59 0.72*** 5.63 0.69*** 5.45 0.70*** 5.43
IndVol 0.42** 1.97 0.42* 1.94 0.38 1.59 0.37 1.58 0.41* 1.80 0.41* 1.80
N 25,322 25,322 25,322 25,322 25,322 25,322
Adj R2 54.76% 54.81% 54.39% 54.55% 54.77% 54.82%
163
Table 16. Risk–taking Incentives and Shareholder Monitoring
Panel A reports results of estimating tobit regressions of RiskIncentive as a function of three proxies for shareholder
monitoring. See Appendix B for variable definitions. The dependent variable RiskIncentive is expressed in %. t-
statistics are based on standard errors clustered by firm and year to correct for time-series and cross-sectional
dependence respectively. ***, **, and * denote statistical significance at the 0.01, 0.05, and 0.10 levels (two-tail)
respectively.
Proxy for ShrMonit pctDED pctACT pctLT
Variable coef t–stat coef t–stat coef t–stat
Intercept –1.61*** –13.78 –1.61*** –13.03 –1.61*** –13.19
ShrMonit 0.32** 2.46 1.15*** 5.33 0.05** 2.12
ReturnIncentive 161.80*** 24.23 161.36*** 24.00 161.42*** 24.00
VPortf 0.00 –0.82 0.00 –0.20 0.00 –0.49
CashComp –0.004** –2.17 –0.003* –1.84 –0.003* –1.79
Age 0.0004** 1.99 0.0005*** 2.64 0.0005** 2.49
Tenure –0.01*** –18.36 –0.01*** –19.14 –0.01*** –19.17
Size –0.03*** –24.12 –0.03*** –23.75 –0.03*** –23.56
BM 0.003*** 4.73 0.003*** 4.66 0.003*** 4.66
Leverage 0.04*** 3.56 0.05*** 7.37 0.05*** 4.06
ROA –0.09*** –11.97 –0.09*** –11.68 –0.09*** –11.67
Volatility 0.11*** 3.66 0.10*** 3.42 0.11*** 3.70
IndustryVol 0.19*** 2.89 0.22*** 3.02 0.22*** 2.98
N 25,322 25,322 25,322
Adj R2 74.23% 74.13% 74.09%
164
Table 17. Propensity-score Matched Pair Analysis
This table presents results of the propensity score matching analysis. Panel A presents statistics of the
treatment and control samples, formed by 11,461 matched pairs (10% of the pairs are left out to improve
covariate balance). For each subsample, treatment (Trmt) and control (Ctrl) groups are formed using Derigs
(1988) algorithm, which forms pairs by minimizing propensity score differences and maximizing treatment
differences. t-statistics are based on standard errors clustered by firm and year to correct for time-series
and cross-sectional dependence respectively. Panel B presents the difference in means and medians between the
treatment (Trmt) and control (Ctrl) groups for research and development (R&D) and idiosyncratic volatility (IdVol).
The propensity score is the conditional probability of receiving some level of treatment given the observable covariates
(control variables) using the specification in equation (12). Γ is the boundary odds ratio required to compute a
Wilcoxon p-value = 0.10. Γ values quantify the amount of hidden bias necessary to alter the statistical significance (p
= 0.10) that results from the assumption that two observations with identical propensity scores have an equal
probability of receiving treatment. Γ is only computed where the t-statistic is statistically significant (i.e., p-value <
0.10) under an assumed odds ratio of 1.00. We use three proxies for shareholder monitoring (ShrMonit), namely
pctDED, pctACT and pctLT (see Appendix B). The first subsample includes matched pairs for which the treatment
observation has higher degree of shareholder monitoring than its matched control (DShrMonit ≥0). The second
subsample includes matched pairs for which the treatment observation has lower degree of shareholder monitoring than
its matched control (DShrMonit <0). The last set of columns shows how differences in risk-taking (measured by IdVol
and R&D) between the treatment and control groups vary across both subsamples (namely DShrMonit ≥0 and
DShrMonit <0). t-statistics are based on standard errors clustered by firm and year to correct for time-series and
cross–sectional dependence respectively.
Panel A. Descriptive Statistics of Treatment and Control Samples
Means Medians
Trmt Ctrl t-stats Trmt Ctrl t-stats
Outcome R&D 0.11 0.09 1.98 0.06 0.03 5.37
variables IdVol 0.52 0.43 3.28 0.46 0.33 6.83
Treatment variable RiskIncentive 0.005 0.002 6.67 0.003 0.001 7.25
Other PctDED 0.05 0.04 1.18 0.00 0.00 0.26
Experimental PctACT 0.02 0.01 2.24 0.01 0.01 2.49
variables PctLT 0.33 0.30 1.61 0.31 0.25 1.84
ReturnIncentive 0.01 0.01 –0.01 0.01 0.01 –0.32
VPortf 46.00 53.66 –1.19 10.22 11.89 –1.78
CashComp 0.90 0.90 –0.01 0.61 0.60 –2.26
Control Age 55.10 55.87 –3.56 55.00 56.00 –1.70
variables Tenure 7.30 7.16 0.76 5.30 5.30 0.00
Size 6.20 6.17 0.17 6.07 6.07 0.001
BM 0.54 0.57 –0.98 0.44 0.47 –2.26
Leverage 0.20 0.21 –1.24 0.14 0.16 –1.78
ROA 0.05 0.06 –0.62 0.09 0.09 –0.32
165
Panel B. Difference in differences
ShrMonit ≥0 ShrMonit <0 Difference
Variable (y) Trmt Ctrl Diff (y1) t-stats Trmt Ctrl Diff (y2) t-stats y1–y2 t-stats
Pct
DE
D
R&Dt+1 Mean 0.11 0.11 0.001 0.06 0.13 0.07 0.060 4.37 –0.059 –4.16
Median 0.05 0.04 0.017 1.88 1.2 0.07 0.02 0.047 12.56 2.1 –0.025 –7.29
IdVolt+1 Mean 0.51 0.49 0.018 0.63 0.55 0.38 0.167 9.90 –0.150 –19.17
Median 0.43 0.39 0.046 2.41 1.3 0.48 0.30 0.180 14.79 3.5 –0.111 –18.22
ShrMonit Mean 0.06 0.01 0.051 4.42 0.02 0.09 –0.069 –13.63
Median 0.03 0.00 0.029 1.32 0.00 0.07 –0.072 –6.10
Pct
AC
T
R&Dt+1 Mean 0.09 0.12 –0.030 –6.82 0.16 0.07 0.092 4.35 –0.122 –9.27
Median 0.05 0.04 0.014 2.22 1.1 0.08 0.03 0.053 8.64 2.5 –0.031 –9.82
IdVolt+1 Mean 0.48 0.51 –0.031 –12.73 0.58 0.37 0.211 1.49 –0.242 –30.94
Median 0.41 0.41 0.001 0.03 0.50 0.29 0.212 15.71 5.0 –0.179 –31.78
ShrMonit Mean 0.02 0.01 0.016 45.86 0.01 0.02 –0.016 –23.15
Median 0.02 0.00 0.020 21.54 0.00 0.02 –0.020 –14.75
Pct
LT
R&Dt+1 Mean 0.09 0.13 –0.038 –4.75 0.16 0.06 0.097 6.48 –0.135 –10.52
Median 0.05 0.05 0.001 0.16 0.08 0.02 0.057 11.77 2.9 –0.042 –18.46
IdVolt+1 Mean 0.47 0.52 –0.050 –1.98 0.59 0.36 0.229 16.78 –0.279 –36.54
Median 0.40 0.42 –0.016 –0.83 0.52 0.29 0.222 16.96 6.1 –0.204 –29.79
ShrMonit Mean 0.44 0.16 0.283 39.82 0.18 0.46 –0.284 –20.99
Median 0.47 0.09 0.383 26.55 0.12 0.49 –0.371 –15.24
166
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