Optimal Real Option Generation and

Investment-Return Dynamics1

Praveen Kumar

C.T. Bauer College of Business

University of Houston

Houston, TX 77204

pkumar@uh.edu

Dongmei Li

Rady School of Business

University of California, San Diego

La Jolla, CA 92093

dongmei@ucsd.edu

This Version: April 2013

1We thank an anonymous referee for helpful comments. We also thank Heitor Almeida, JonathanBerk, Je¤rey Brown, Louis Chan, Jaewon Choi, Prachi Deuskar, Wayne Ferson, Slava Fos, PaoloFulghieri, Andrew Grant, Richard Green, Eric Ghysels, Dirk Hackbarth, David Hirshleifer, Ger-ard Hoberg, Elvis Jarnecic, Dirk Jenter, Charles Kahn, Nisan Langberg, Michael Lemmon, NeilPearson, Graham Partington, George Pennacchi, Gordon Phillips, Josh Pollet, Je¤rey Ponti¤,Michael Roberts, Laura Starks, Sheridan Titman, Selale Tuzel, Neng Wang, Joakim Westerholm,Toni Whited, Jianfeng Yu, Lu Zhang, Guofu Zhou, seminar participants at University of Illinois(Urbana-Champagne), the USC Conference on Financial Economics and Accounting, and Univer-sity of Sydney for useful comments.

Abstract

Firms strategically use capital investments to generate future growth options, and not just to

convert existing ones. Using a dynamic model, we show that real option generating capital

investments can increase equilibrium expected returns, in contrast to the widely documented

negative investment-return dynamics. Positive investment-return dynamics are more likely

if the new growth options arrive with low instantaneous probability, require large initial

investments, and if there is slow growth in the firm’s existing line of business. We find

empirical support for these and other novel predictions of the model using cross-sectional

tests on a comprehensive sample of firms during 1976-2011.

Keywords Capital investment, Real options, Option generation, Risk

JEL classification codes: G12, G14, G30

1 Introduction

The negative e¤ects of capital investment on subsequent stock returns have recently been

highlighted both theoretically and empirically. A variety of models in the literature predict

a negative equilibrium relation between investment and future returns. In particular, real

options models predict a decline in systematic risk following the exercise of risky growth

options (e.g., McDonald and Siegel, 1986; Majd and Pindyck, 1987; Carlson, Fisher, and

Giammarino (CFG), 2004, 2006) or argue that investment is positively related to the avail-

ability of low risk projects so that the systematic risk of the �rm declines after investment

(e.g., Berk, Green, and Naik (BGN), 1999).1 Meanwhile, a number of empirical studies

present evidence of a signi�cant negative relation between �rms� capital investment and

subsequent stock returns (Titman, Wei, and Xie, 2004; Anderson and Garcia-Feijoo, 2006;

Cooper, Gulen, and Schill, 2008).2

However, existing real options models in the literature largely view the generation of

growth options as exogenous where capital investments essentially exercise available growth

options and convert them into assets-in-place. But in many industries, such as the pharma-

ceutical, hi-tech, and oil and gas industries, �rms use capital investments to strategically and

pro-actively improve the likelihood of generating future growth options. To illustrate, sup-

pose that a pharmaceutical company invests in R&D infrastructure to commercially develop

1Similarly, optimal dynamic investment based on the neoclassical q-theory may exhibit a negative relationbetween investment and future returns (e.g., Liu, Whited, and Zhang, 2009; Li and Zhang, 2010).

2Other empirical studies that include similar results include Xing (2008), Li and Zhang (2010), Titman,Wei, and Xie (2011), Stambaugh, Yu, and Yuan (2011), and Watanabe et al. (2012). Some of these studiesview these results as �anomalies,� and present bevahioral explanations (e.g., Titman, Wei, and Xie, 2004;Cooper, Gulen, and Schill, 2008)). See Cooper and Priestly (2011) for a good survey of this literature.

1

and market a new class of drugs.3 With this type of investment, the �rm is not converting

an available growth option � indeed, the �rst available commercial opportunity may be

many years in the future. Rather, it is positioning itself to exploit the commercial opportu-

nities that may emerge from the new scienti�c discovery. Similarly, capital investment by a

company like Apple to create the capacity to develop products that build on successful inno-

vations � for example, the integration of smart phones with the iPod platform � in�uence

the likelihood of future growth options (Adner, 2012).

More generally, the notion that capital investments can generate real options is consis-

tent with the view that innovations not only present immediate growth opportunities but

are often the source of ideas and knowledge spillovers that result in the generation of new

growth opportunities (Schumpeter, 1942; Maclaurin, 1953). It is also consistent with the

industrial organization and strategy literatures. Long-range R&D capacity is considered

central to maintain �rst-mover advantages (Lieberman and Montgomery, 1987) and to real-

ize economies of scope and extract rents from the internal and external knowledge spillovers

of innovations (Henderson and Cockburn, 1996). And Christensen (1997) relates R&D ca-

pacity to the development of �disruptive� innovations that start at periphery of industries

but eventually leap-frog to displace the accepted technologies or products. (For expositional

ease, we will call such real options generating capital investments as ROG investments).

Standard �nance intuition suggests that the e¤ects of ROG investments on subsequent

3Under current GAAP (generally accepted accounting principles), U.S. �rms are required to expense mostR&D-related costs. However, �rms need to capitalize certain types of R&D costs, such as construction oflong-range research facility, purchase of R&D equipment with alternative future use, and patents acquisition.These costs are included in capital expenditure and total assets. The depreciation and amortization of thesecosts are included in R&D expenditure over their useful life.

2

expected returns need not necessarily be negative.4 In contrast to investment that exercises

risky growth options and converts them to assets-in-place with lower systematic risk, ROG

investments may raise the systematic risk of the �rm�s asset mix. For example, if the

new R&D facilities or patent acquisitions signi�cantly increase the likelihood of future risky

growth options, then it is not apparent that the expected returns will fall subsequent to

investment. That is, ROG investments may lead to return-reversals relative to the negative

relation of capital investment and subsequent stock returns highlighted in the literature.

Of course, this intuition needs further scrutiny. Do all ROG investments lead to return-

reversals relative to the negative relation seen in the literature? Introspection suggests

not. For there to be return-reversals, the systematic risk of the �rm�s asset mix has to

increase, which suggests that the ROG investment has to signi�cantly raise the likelihood of

risky �nancial outlays or investments to develop growth options in the future. However, an

equilibrium analysis of such return-reversals remains to be explored; in particular, identifying

su¢ cient conditions for return-reversals in terms of observable �rm characteristics is an open

issue.

In this paper, we provide a model of real option generation (ROG) by capital investment

that relates �rm characteristics to the possibility of return-reversal � that is, capital in-

vestments have a positive e¤ect on the �rm�s equilibrium expected return by increasing its

systematic risk. To facilitate comparison with the literature, our framework builds on real

options models such as BGN (1999) and CFG (2004), by incorporating heterogeneity in the

4We note that the ROG envisioned here is distinct from the notion of compound options (or an optionon options), where the exercise of the �rst option will decrease risk. For example, the concept of a com-pound option is more applicable to multiple stages of clinical trials in pharmaceutical companies rather thandevelopment of a commercial ecosystem built around a new class of drugs.

3

types of capital investments. Speci�cally, we consider optimal capital investments by two

types of �rms. The �rst type of �rms are low innovation potential (LIP) �rms, such as �rms

with stable market power in technologically mature industries, where real investments con-

vert a �xed number of available growth options into assets-in-place � for example, capacity

expansion options (CFG, 2004). The second type are high innovation potential (HIP) �rms

� such as �rms in technologically driven real options-intensive industries (see, e.g., Grullon,

Lyandres, and Zhdanov, 2012) that have the �nancial ability to maintain R&D programs

and develop innovations � that can make ROG investments. In e¤ect, the HIP �rms have

an option to invest in an ROG project. Both types of �rms optimally exercise their real

options.

The ROG model con�rms the negative capital investment-return dynamics of LIP �rms,

similar to the relation highlighted in the literature. However, for HIP �rms their ROG

investments can increase expected returns by raising the systematic risk of the �rm. In

essence, the su¢ cient conditions for ROG investments to raise equilibrium expected returns

are that the generated real options be �large�in the sense that: (1) the investment required

to exercise the new growth options (when they arrive) are high relative to the initial ROG

investment and (2) the probability of the arrival of growth options immediately after the

ROG investment is not too high. These conditions will typically be satis�ed in cases where

the ROG investment is designed to develop the �rm�s long run innovation capacity (IC) by

undertaking relatively large innovation programs, for example the pursuit of �blockbuster�

drugs by pharmaceutical companies (Achilladelis, 1999) or fundamental improvements in

4

deep-sea resource extraction technologies by oil and gas companies.5 In addition, ceteris

paribus the return-reversal is more likely if the �rm�s existing business lines are indicating

slowing growth prior to the ROG investment.6

Intuitively, if the cost of exercising future growth options is small, then these options

are less risky and ceteris paribus the value of the �rm after the ROG investment will be

relatively high, and return-reversals are less likely. Similarly, if the ex ante probability

of immediate arrival of growth options (following the ROG investment) is high, then the

value of the company, conditional on the ROG investment, will also be large, reducing the

realized returns in the period after that investment, so that, ceteris paribus, return-reversal

are less likely. Finally, the return subsequent to the ROG investment will ceteris paribus

be negatively related to the value of the �rm�s initial lines of business, so that the return-

reversal is less likely if the value of the current assets-in-place is growing rapidly. Two

good illustrations of these conditions are: A large pharmaceutical �rm that faces expiration

of patents in its current blockbuster drugs and undertakes long range R&D investment to

develop and market new blockbuster drugs; and, a microchip producing company that faces

cheap imitation of its current frontline product and undertakes a major R&D e¤ort to develop

an entirely new generation of microchips.

To our knowledge, ours is the �rst study to develop theoretical predictions on return-

reversals � that is, regarding the conditions for positive real investment-return dynamics �

based on a real options model. In addition, building on BGN (1999) and CFG (2004, 2006)

5The IC concept has been used in the R&D strategy literature and in the literature on economic growthof nations and geographic regions (see Furman, Porter, and Stern, 2002).

6Kumar and Li (2013) distinguish between ROG investments and IC investments; the latter are thoseROG investments that are capable of generating return-reversals, i.e., increase the �rm�s expected returnssubsequent to the capital investment.

5

we develop novel testable predictions regarding the negative investment-return dynamics of

LIP �rms. For example, the real options models in the literature suggest that the negative

relation of capital investment to subsequent returns will be increasing in magnitude with

the systematic risk of the �rm (for large capital investments) and with the investment costs

(following the intuition of CFG (2004)). In addition, if earnings are positively autocorrelated,

which is consistent with the data (Watts, 1975; Gri¢ n, 1977), then the relation of investment

to subsequent returns will be increasing with earnings (or sales) prior to the investment (see

Section 3.1). However, these predictions for the LIP �rms also remain to be examined

empirically.

We, therefore, empirically test the predictions of our model using the R&D intensity

(i.e., R&D expenditures scaled by sales) as the proxy for innovation potential; we focus on

R&D intensity because level of R&D expenditures is the most widely used proxy for �rms�

innovative e¤ort (see, e.g., Rogers, 1998). Using a comprehensive sample of �rms from 1976-

2011,7 and cross-sectional Fama and Macbeth (1973) regressions, we �nd support for many

of the main predictions of the model.

For the low R&D intensity (or LIP) �rms, we �nd that the negative investment-return

relation is signi�cantly moderated (or is less negative) for �rms that had higher ROA or asset

turnover prior to the capital investment, but higher systematic risk �rms with relatively large

capital investments ceteris paribus exhibit signi�cantly greater negative investment-return

dynamics, as do �rms in industries with high capital adjustment costs (see Hall, 2004). These

empirical �ndings are consistent with main predictions of the model, and also new to the

7We start our sample in 1976 because the accounting treatment of R&D expense reporting was standard-ized in 1975.

6

literature.

Meanwhile, for the high R&D intensity (or HIP) �rms, the returns in the year following

investment are signi�cantly and negatively related to the lagged earnings growth � that

is, the likelihood of return-reversals are less likely if the earnings growth prior to the ROG

investment was high. Moreover, post-investment returns by HIP �rms are signi�cantly and

positively related to �rm size, as noted also by Kumar and Li (2013), and are also higher

ceteris paribus in industries with higher development costs. These results are also consistent

with the predictions of the theoretical model and introduce a new set of empirical facts to

the literature because the investment-return dynamics induced by ROG investment have

received little attention earlier. In particular, the empirical results with respect to HIP �rms

suggest that it is important to distinguish between generated real options that require large

and risky �nancial outlays for further development � such as those undertaken by large

and well-funded �rms � and those that require relatively small additional investment or can

be converted for cash � such as when small �rms sell out to acquirers (Brau, Francis and

Kohers, 2003; Poulsen and Stegemoller, 2008).

While the existing real options models in the literature generally predict a negative

equilibrium relation between investment and future returns, we show that the real options

approach can be applied meaningfully to model the strategic (and risky) generation of growth

options that appears to be an important aspect of many (high innovation potential) indus-

tries, as suggested by the literatures on innovation and industrial organization. In particular,

the extended real options framework predicts a positive relation of capital investments to

stock (under speci�ed conditions), and this prediction is supported by an empirical analy-

7

sis. In sum, our analysis extends the literature by providing a theoretical foundation for

and new empirical evidence on the signi�cant cross-sectional heterogeneity in the relation of

capital investment to subsequent stock returns, and potentially helps di¤erentiate existing

explanations for investment-related anomalies (see, e.g., Cooper and Priestley, 2011).

We organize the paper as follows. Section 2 describes the basic model. Section 3 charac-

terizes the optimal capital investment policies, and analyzes the determinants of the change

in equilibrium returns following investment. Section 4 discusses the empirical tests, and

Section 5 concludes.

2 The Model

We distinguish between two types of �rms. The �rst type of �rms have a �xed number of

available growth options; exercising these options requires capital investments and converts

them into assets-in-place. However, converting the growth options does not generate any

new growth options. A useful illustration of such situations are �rms with market power in

technologically mature industries (�cash cows�) having a �xed number of capacity expansion

options that scale up pro�ts in their well developed markets, but do not generate new

technological innovations or open new lines of business. For expositional ease, we call such

�rms low innovation potential (LIP) �rms.

The second type of �rms are in industries that are rich in technology-driven growth op-

tions or innovation possibilities. In particular, these �rms can pro-actively choose to make

capital investments to develop their capacity to generate and commercialize new technolog-

ical or product design �breakthroughs� or innovations. Such situations are illustrated by

8

investments in building long range R&D infrastructure and acquiring patents that build the

�rm�s innovative capacity � the ability to generate growth options in the form of risky but

high expected-return innovations. For expositional ease, we call such �rms high innovation

potential (HIP) �rms. Moreover, to distinguish between capital investments of LIP �rms �

that exercise available growth options � and capital investments that can build innovation

capacity, we call investments by HIP �rms �ROG investments.�

For simplicity, we model the typical LIP �rm with one capacity expansion option. Mean-

while, the typical HIP �rm can make capital investment that will stochastically generate a

growth option in the future, which (if it arrives) can then be exercised with further develop-

ment expenditures. Both types of �rms operate in discrete time with an in�nite horizon, and

optimally make their capital investment decisions. We now describe these �rms in greater

detail.

2.1 Low IP Firms

Cash-�ows in each period t 2 f0; 1; 2; :::g depend on the size of the assets, which in this

stylized model are represented by the capital stock Kt. At the outset, i.e., at the beginning

of t = 0, each LIP �rm has the capital stock K0 = K`: However, LIP �rms have an option

to make an irreversible investment and expand their assets to the capital stock Kh > K` by

expending the �xed cost FL: These capacity expansion (or investment) costs include both

the capital costs and the adjustment costs (see Hayashi, 1982; Caballero and Engle, 1999).8

For simplicity, there is no capital depreciation. Hence, Kt 2 fK`; Khg; moreover, because of

8For notational parsimony, we do not make the components of the investment costs explicit.

9

the irreversible nature of the capacity expansion, if Kt = Kh, then Kt+i = K

h; i = 1; 2:::

The per-period cash-�ows for LIP �rms are stochastic and depend on a random earnings

(revenue-side) state variable fxtg that follows a martingale process:

xt+1 = xt + "x;t+1 (1)

where, the innovations f"x;t+1g are identically and independently normal with mean zero

and variance �2x: And, the cash-�ows at t are:

CLt = GL(KL

t ) exp(xt ��2x2� �L) (2)

Here, GL(�) is a strictly increasing function, so that GL(Kh) > GL(K`), while �L is the

unit production cost.9 The cash-�ow function in (2) is consistent, for example, when �rms

have a local monopoly and the pro�t function is strictly increasing in output (e.g., CFG,

2004). Furthermore, like CFG (2004), but unlike BGN (1999), the cash �ows depend on a

persistent earnings state variable. The positive serial correlation in earnings is consistent

with the observed earnings processes (e.g., Watts, 1975; Gri¢ n, 1977).

Finally, we allow the possibility of stochastic obsolescence that may force the �rm to

shut down irreversibly. For operating �rms the probability of surviving such obsolescence is

0 < �L < 1 per period, and this probability is independent of all other variables.

9For notational ease, the unit costs do not depend on the capital stock. However, our results are nota¤ected by allowing the unit costs to depend on the capacity level.

10

2.2 High IP Firms

High IP �rms start with capital stock Qo; but have an option to invest in innovative capacity

that can be a source of future but stochastically arriving growth opportunities in a new but

related market. The initial capital generates per-period cash-�ows that are stochastic and

depend on a state variable fytg :

CHo;t = GHo (Qo) exp(yt �

�2y2� �Ho ) (3)

Here, GHo (Qo) > 0; �Ho are the unit costs, and the state variable follows the martingale

process yt+1 = yt + "y;t+1, where the innovations f"y;t+1g are identically and independently

normal with mean zero and variance �2y: There is also stochastic obsolescence, given by the

per-period survival probability �o, that forces an irreversible closures of the �rm�s operations

in its initial market. To sharpen the contrast between the ROG investment option versus

an expansion option, we exclude the availability of capacity expansion options in the initial

line of business.

We model the ROG investment option as one that stochastically generates future growth

options. Speci�cally, at any t � 0, a HIP �rm can choose to make an ROG investment

of FHn that can stochastically generate a growth opportunity in the future in the following

sense. Conditional on the investment, the arrival of the innovation is stochastic and follows

a Poisson process with a �hit rate��: Thus, if the investment option is exercised at t, and

conditional on the innovation not having arrived till some s � t+1; the probability that the

innovation will arrive during the current period is (�) � (1�exp(��)), and this probability

11

is independent of other random variables in the model.10

If the innovation arrives at some period s � t + 1 (where t was the period of the ROG

investment), then the �rm has the option to develop and market the innovation. But doing

so requires capital input Qn at the cost In; and generates cash-�ows that depend on a

stochastically evolving state variable fzs+ig; i = 0; 1; 2::; that is positively related to the

revenue from the innovation:11 Thus, if the innovation is implemented at � � s, then per-

period cash-�ows thereafter are:

CHn;�+i = GHn (Qn) exp(z�+i �

�2z2� �Hn ); i = 0; 1; 2; :: (4)

Here, GHn (Qn) > 0; �Hn are the unit costs in the production of the innovation, and the state

variable follows the martingale process zj+1 = zj + "z;j+1, where the innovations f"z;jg are

identically and independently normal with mean zero and variance �2z: As with the other

markets, there is a possibility of stochastic obsolescence in the new market when the �rm

starts production and cash-�ow generation. Such obsolescence forces the �rm to shut down

irreversibly and its presence is modeled through the survival probability of 0 < �n < 1 per

period.

In the spirit of our model, which views the stochastically arriving growth opportunity

following the ROG investment (FHn ) as innovations, we assume that the �rm does not observe

the state variable z � that represents the market condition or expected revenues � until

10The Poisson process is widely used in the literature on the economics of innovation to model the stochasticarrival of innovations (see Reinganum, 1989).11Note that the timing assumptions on the arrival of the innovation following the ROG investment at t is

that the �rm must wait at least one period for the innovation to be ready at t+1; an event that occurs withthe probability (1 � e��): This appears to be the most plausible timing convention because it emphasizesthe point that the �rm does not have the innovation in hand when it makes the ROG investment at t:

12

the arrival of the innovation. Through this assumption, we model the idea that the nature

of the market is not fully clari�ed till the development or �arrival�of the innovation at the

(random) date s � t + 1: However, following the arrival of the innovation at s; the �rm

observes fzs+ig so that the decision to exercise the new growth option (with an exercise

price of In) at any � � s is measurable with respect to fzs;:::; z�g:

Meanwhile, the decision to make the ROG investment � that is, the exercise of the

initial growth option � will depend on signals that the �rm receives regarding the potential

value of future innovations. These signals sometimes may be positively related to the �rms�

current business � for example, the relation of iPhone to the iPod in the case of Apple.

However, in many other cases, the innovation may be either essentially independent of the

current business � for example, when the �rm invests in R&D to enter a new business � or

even be negatively related to state of the current business � for example, IBM�s investment

in R&D for personal computers that were substitutes for its electric typewriter business. We,

therefore, take the agnostic approach and assume that there are signals f�tg � commonly

observable to the �rm and the �nancial markets � that are correlated with the revenues

from the potential innovation, namely, fzig: And for parsimony these signals are su¢ cient

statistics (see, e.g., DeGroot, 1971) of all other available information.

Speci�cally, we assume that the signals f�tg are identically and independently normal

(with mean �� and variance �2�) such that, for any t and conditional on �t; the distribution

of zi; i � t+ 1; is normal with the mean and variance:

E[zi �t] = �z + ��t; Var[zi �t] = !�2z (5)

13

where �z; �; and ! are positive constants.12 While the stationary stochastic structure on the

signals is notationally convenient, our main results are qualitatively una¤ected and will hold

if we allow f�tg to be serially correlated.13

Figure 1 displays the time-line for the ROG investment, innovation arrival, and exercise

of the innovation-based growth option.

2.3 Pricing Kernel and Risk

We assume that there is a stochastic discount factor (or pricing kernel) fmtg that follows:

mt+1 = mt exp(�r ��2m2� "m;t+1) (6)

The innovations f"m;tg are serially independent normal variables with mean zero and variance

�2m: Here, r is a positive constant which is is the constant equilibrium risk-free rate. Note

that:

Et[exp(�r ��2m2� "m;t+1)] = exp(�r) (7)

so that the continuous time return on a claim on a riskless asset is:

� ln�Et[mt+1

mt

]

�= r (8)

Cash-�ows of both types of �rms (LIP and HIP) are subject to systematic risk because the

12In the usual way, these constants can be expresssed in terms of the parameters of the underlying bivariatenormal distribution.13Note that because the signals are su¢ cient statistics of all other available information, it follows that

Pr(zi j �t; yt) = Pr(zi j �t):

14

pricing kernel innovations f"m;tg have a positive, but constant, contemporaneous covariance

with the revenue shocks. This covariance is represented by positive parameters or �betas�

�j � Cov("m;t; "j;t); j 2 fx; y; zg:14

3 Investment Policy and Changes in Equilibrium Re-

turns

Our main focus in this section is to examine the e¤ect of investment on the change in

equilibrium returns following investment. Therefore, we need the equilibrium returns both

preceding and following the investment decision. And, to do so, we have to characterize the

optimal exercise policy, which allows �nancial markets to determine valuation (and expected

returns) prior to the investment. We now perform this analysis separately for both types of

�rms.

3.1 Low IP Firms

We �rst derive the equilibrium returns following the exercise of the investment option, be-

cause in our stylized model this exhausts any further investment possibility and leads to a

stationary risk premium.

14While theoretically betas can be negative, the assumption of positive betas is empirically appealing andallows us to parsimoniously represent comparative statics with respect to systematic risk. We �nd that only6% of our sample have negative betas.

15

3.1.1 Equilibrium Returns Following Investment

If the �rm invests to exercise the capacity expansion option at t, then for s � t + 1; the

cash-�ows (if the �rm is in operation) are:

CLs = GL(Kh) exp(xs �

�2x2� �L) (9)

Hence, the price of a security purchased at any s � t+1 and held for one period with payo¤s

�LCLs+1 is:

pLs (xs) = �LEs[ms+1

ms

CLs+1] (10)

Using the pricing kernel (6) and (9), and the martingale assumption on the state variables

Es[xs+1] = xs, this price is:

pLs (xs) = �LGL(Kh) exp(xs � �L � (r + �x)) (11)

Meanwhile, given the existence of the positive pricing kernel, for any return from s to s+1;

Rs;s+1, we must have

Es[Rs;s+1] = er[1� Covs(ms+1

ms

; Rs;s+1)] (12)

Then, recognizing that Covs(ms+1

ms; Rs+1) = Es[ms+1

msRs+1]�Es[ms+1

ms]Es[Rs+1] and that RLs+1 =

CLs+1=pLs ; we get:

Es[RLs;s+1] =�LG

L(Kh) exp(xs � �L)�LGL(Kh) exp(xs � �L � (r + �x))

= exp(r + �x) (13)

16

In sum, for low IP �rms there is no investment uncertainty left after the exhaustion of growth

options, resulting in a stationary risk premium given by the systematic risk of the cash-�ows,

represented here by �x:

We turn, next, to derive the optimal investment policy for low IP �rms.

3.1.2 Optimal Investment Policy

The optimal investment policy is the solution to an optimal stopping time problem. To

express this concisely, at any t prior to the exercise of the investment option with the state

variable realization xt; let V L`;t(xt) and VLh;t(xt) denote the present values of expected cash-

�ows for s = t; :::; with the capital-stocks KLs = K

` and KLs = K

h, respectively. Given the

foregoing, with �xed capital stocks, these values are:

V Lj;t(xt) = GL(Kj)E

" 1Xs=t

�s�tL

ms

mt

exp(xs ��2x2� �L) xt

#; j = `; h (14)

From the martingale assumption on the state variable, E[xs xt] = xt; s = t+1; ::: Using this

and iterated expectations, (14) can be written (see the Appendix):

V Lj;t(xt) = GL(Kj) exp(xt � �L)

1Xs=t

�s�tL exp(�(s� t)(r + �x)); j = `; h (15)

However, we note that:

1Xs=t

�s�tL exp�((s� t)(r + �x)) =�L exp(�(r + �x))

1� �L exp(�(r + �x))� �L (16)

17

Then, at any t the capacity expansion option, if still available, will be exercised if xt is such

that V Lh;t(xt)� V L`;t(xt) � FL. Using (15)-(16), we can use this condition to characterize the

optimal exercise policy.

Let,

x� = �L + ln

�FL

�L[GL(Kh)�GL(K`)]

�(17)

Hence, the optimal stopping time or exercise date is t� = inftft xt � x�g: It is straightforward

to show that the exercise threshold state x� is increasing in the cost of capital or post-

expansion return (r + �x), but is decreasing in GL(Kh) � GL(K`). These properties are

consistent with the intuition that, because of positive serial correlation in expected pro�ts,

the optimal exercise threshold state is negatively related to the value gain from expansion.

Therefore, for any t < t�; the ex-dividend value �V Lt (xt), i.e., the value of future cash-�ows

(for s = t + 1; :::); can be derived as the value of a one-period asset that, at t + 1; �pays�

V L`;t+1(xt+1) if xt+1 < x� but �pays�V Lh;t+1(xt+1)� FL if xt+1 � x� : Hence,

�V Lt (xt) = Et[mt+1

mt

V L`;t+1(xt+1) xt+1 < x� ] + Et[

mt+1

mt

(V Lh;t+1(xt+1)� FL xt+1 � x� ] (18)

Further analysis of (18) yields a more succinct representation of �rm valuation and equilib-

rium returns prior to investment. Let, �(� xt) be the cumulative distribution function for a

normal distribution with the mean xt and the variance �2x: Then,

Proposition 1 Prior to exercising the investment option (i.e., for any t < t�);

�V Lt (xt) = exp(xt � �L � (r + �x))DL(x� xt)� e�rFL(1� �(x� xt))

18

where, DL(x� xt) � �L[GL(K`)�(x� xt) +GL(Kh)(1� �(x� xt)]:

Using the �rm value representation in Proposition (1), and using the return representation

in (12), we can derive the expected one-period return on LIP �rms prior to the exercise of

the asset expansion option. Moreover, this return exceeds the stationary return exp(r+ �x)

following the asset expansion.

Corollary 1 Prior to exercising the investment option (i.e., for any t < t�);

Et[RLt;t+1] =exp(xt � �L)DL(x� xt)� FL(1� �(x� xt))

�V Lt (xt)> exp(r + �x)

Indeed, from Corollary (1), for low IP �rms we can compute the change in the equilibrium

returns from t� � 1 (the period immediately preceding the asset expansion) to immediately

succeeding the expansion, i.e., �L(t� � 1; t� + 1) � Et��1[RLt��1;t� ]� Et� [RLt�;t�+1] as:

�L(t� � 1; t� + 1) =FL(1� �(x� xt))(e�x � 1)

�V Lt (xt)(19)

Using the foregoing, we can do comparative statics on �L(t� � 1; t� + 1); which we can

then potentially test with the data.

Proposition 2 The fall in equilibrium return subsequent to investment (i.e., �L(t��1; t�+

1) > 0) is increasing in magnitude with the investment cost FL; but decreasing in magnitude

with the �rm�s earnings state xt prior to the investment. The negative investment-return

relation is also greater for �rms with higher risk �x if GL(Kh)�GL(K`) is su¢ ciently large:

19

While there is a large empirical literature documenting the negative cross-sectional rela-

tion of capital investment to subsequent returns, to our knowledge the predictions of Propo-

sition 2 remain to be directly tested. The prediction with respect to the investment cost

(FL) implies that the decline in post-investment returns will be ceteris paribus greater when

capital is tight (e.g., high interest rates) or in industries with large capital adjustment costs

(Holt et al., 1960; Cooper, Haltwinger and Power, 1999). And, because of the well known

dynamic relation between book assets and earnings, Proposition 2 also implies that ceteris

paribus high book-to-market (BTM) �rms prior to capital investment will exhibit smaller

declines in returns. This prediction appears consistent with Kumar and Li (2013) who �nd

that among the low R&D �rms � corresponding to the LIP �rms here � the negative e¤ect

of capital investment appears marginally smaller among the high BTM �rms.

Figures 2-4 graphically illustrate the time-evolution of the typical LIP �rm�s equilibrium

returns by simulating the earnings shocks fxtg: Here, we take GL(KL) =pKL and the

parameterization of the other parameters imply a steady state cost of equity of about 11.6%.

We note that in our model the equilibrium returns will rise prior to the capital investment

if there is a signi�cant likelihood of exercising the growth option in the next period, condi-

tional on the current earnings state xt: Because of the positive serial correlation in earnings,

expected returns begin to rise as xt approaches close to the critical exercise value x�. Thus,

in all three �gures, we see a �spike� in expected returns immediately prior to the capital

investment and the expected returns �collapse�immediately thereafter to their steady state

values, since there is only one capacity expansion option.

However, Figures 2-4 show somewhat distinct returns patterns in the pre-capital-investment

20

phase because the critical exercise values x� are di¤erent. Speci�cally, Figure 3 assumes a

lower average cost of investment compared with Figure 2. In the former, the per unit invest-

ment cost FL=(KH � KL) is one-half of the cost assumed in Figure 2. Hence, the critical

earnings threshold in Figure 3 is lower than that in Figure 2, so that we observe more return

�spikes� prior to the actual investment event. These spikes occur because the xt values

portend likelihood of exercise next period, but the earnings realizations next period do not

cross the threshold. In Figure 4, the critical exercise value is even lower than that in Figure

3 because of the still lower average investment cost, and we see many return spikes prior to

the actual investment.

3.2 High IP Firms

In this case, it is useful to �rst characterize the optimal investment policy and then derive

the change in the equilibrium return subsequent to investment through the exercise of the

investment option.

3.2.1 Optimal Investment Policy

For the HIP �rms, the ROG investment FHn does not directly in�uence the expected cash-

�ows from its initial business. Hence, the investment decision is governed by comparing the

state-dependent present value of expected of cash-�ows from the new opportunity with the

investment cost (FHn ): However, we recall that the ROG investment stochastically generates

a growth option where the �rm can optimally time the implementation of the innovation

(when it arrives). Hence, to derive the optimal ROG investment policy, we �rst derive the

21

optimal exercise policy for the growth option (conditional on its arrival).

Suppose, as described above, the ROG investment is made at t and the innovation arrives

at some s � t + 1. If the innovation is implemented at any � � s; then (based on the

description of the growth opportunity in Section 2.2) the present value of expected cash-

�ows is:

WHn;� (z� ) = G

Hn (Qn)E

" 1Xi=�

�i��n

mi

m�

exp(zi ��2z2� �Hn ) z�

#(20)

And, using analytics similar to Section 3.1.2, we can write:

WHn;� (z� ) = exp(z� � �Hn )GHn (Qn)�Hn (21)

where �Hn � [�n exp(�(r+�z))]=[1��n exp(�(r+�z))]: Then, noting thatWHn;� (z� ) is strictly

increasing in z� , and applying an argument similar to (17), it follows that for z� = �Hn +

ln�

In�Hn G

Hn (Qn)

�, the optimal exercise time for the growth option is � � = inf�f� � s j z� � z�g:

Consider now the value of a security with a complete claim to cash-�ows from the new

business, conditional on making the ROG investment at t with the state variable �t, which

we denote by �V Hn;t(�t): Notice that the joint probability that an innovation arrives at t + 1

and will be exercised at that date is (�) Pr(zt+1 � z� �t): And, the value at t of this payo¤

is:

E�mt+1

mt

�WHn;t+1(zt+1)� In

�zt+1 � z�; �t

�(22)

In (22), as before, we recognize that the present expected value of cash-�ows from implement-

ing the innovation at t+ 1 is contingent on the state variable zt+1: Then using a derivation

similar to that given in Proposition (1), we can write:

22

�V Hn;t(�t) = (�)(1� �z(z� �t))�exp(�z + ��t � �Hn � (r + �z))GHn (Qn)�Hn � Ine�r

(23)

Now, the �rm will only exercise the ROG investment option if �V Hn;t(yt) � FHn : But it is ap-

parent from (23) that �V Hn;t(�t) is increasing in �t because zt+1 and �t are positively correlated

and hence �z(z� �t) is a decreasing function of �t: We can thus characterize the optimal

stopping time for the ROG investment as follows.

Proposition 3 There exists �� such that the optimal ROG investment policy is to invest

FHn at the �rst date t� such that �t � ��; that is, the optimal stopping time for the exercise

of the growth option is t� = infift �t � ��g:

3.2.2 Change in Returns Following ROG Investment

We �rst compute the returns following the ROG investment (FHn ) at t�: Note that the �rm

now has two sources of cash-�ows: it�s original business and the new growth option generating

business. For the former, it is easy to compute the ex-dividend value to be:

�V Ho;t�(yt�) = exp(yt� � �Ho � (r + �y))GHo (Qo)�H;o (24)

where, �Ho � [�o exp(�(r + �y))]=[1 � �o exp(�(r + �y))]: Meanwhile, the value of the new

opportunity �V Hn;t�(yt�) is given by (23). Hence, the total �rm value for claims to cash-�ows at

t� + 1; :::; �V Ht� (yt� ; �t�) =�V Ho;t�(yt�) +

�V Hn;t�(�t�), and using analytics used above, we can show

23

that:

Et� [RHt�;t�+1] =exp(yt� � �Ho )GHo (Qo)�H;o + �Hn;t�(�t�)

�V Ht� (yt� ; �t�)

�Hn;t�(�t�) = (�)(1� �z(z� �t�))fexp(�z + ��t� � �Hn )GHn (Qn)�Hn � Ing (25)

Turning, next, to the one-period return prior to the ROG investment, note that at any

i < t�; the ROG investment will occur at i+ 1 if �i+1 � ��: But since �i+1 has a stationary

distribution, the ex-dividend value at i is:

�V Hi (yi) = Ei[mi+1

mi

V Ho;i+1(yi+1)] + E[mi+1

mi

( �V Hn;i+1(�)� FHn ) � � ��] (26)

Clearly,

Ei[mi+1

mi

V Ho;i+1(yi+1)] = exp(yi � �Ho � (r + �y))GHo (Qo)�H;o (27)

And we can compute E[mi+1

mi( �V Hn;i+1(�i+1)� FHn ) �i+1 � �� ] as:

exp(�(r + �z))GHn (Qn)�Hn (�)E[(1� �z(z� �)) exp(�z + ��� �Hn ) � � ��]�

(�)E[(1� �z(z� �)Ine�r) � � ��]� (1� ��(��))FHn e�r (28)

Hence, the one-period return at t� � 1 is:

Et��1[RHt��1;t� ] =exp(yt��1 � �Ho )GHo (Qo)�H;o + Hn � (1� ��(��))FHn

�V Ht��1(yt��1)(29)

Hn = (�)E[(1� �z(z� �))fGHn (Qn)�Hn exp(�z + ��� �Hn )� Ing � � ��] (30)

24

Using (25)-(30), we can compute the change in the return immediately preceding and suc-

ceeding the ROG investment, i.e., �H(t� � 1; t� + 1) � Et��1[RHt��1;t� ] � Et� [RHt�;t�+1]: It is

apparent that �H will depend on the relation of the systematic risk of cash-�ows in the new

business � that is, �z � to the risk of cash-�ows from the �rm�s assets-in-place � that is,

�y. There may be situations where it is more likely that �z � �y � for example, when the

post-ROG investment growth options are in high risk industries. But there are also plausible

arguments for the converse, i.e., �z < �y � for example, if the �rm develops on the initial

line of business (as seen in some of the illustrations given above), in which case the post-ROG

investment growth options may be less risky. To avoid any pre-determination of results, we

will therefore take the agnostic view and assume that the systematic risk of the post-ROG

investment cash-�ows is the same as that prior to that investment (i.e., �z = �y):

We now provide su¢ cient conditions for a positive ROG investment and return relation.

Essentially, these conditions are that around the ROG investment event the �rm has not too

high sales growth from its initial business (or assets-in-place); the investment that would be

required to exercise the new growth options (In) is large relative to the ROG investment

(FHn ); and, the likelihood of the arrival and exercise of the new growth option immediately

after the ROG investment (that is, in period t�) is not too high.

Proposition 4 The ROG investment-return relation is positive ( i.e., �H(t��1; t�+1) < 0)

if (1) the earnings growth (i.e., yt� � yt��1) preceding the ROG investment is low; or (2) the

joint likelihood of arrival and exercising of the growth option immediately after the ROG

investment is small; or (3) the future growth option development cost (In) is large relative

to the ROG investment (FHn ).

25

To interpret the conditions of Proposition 4, note that the return subsequent to the

ROG investment will be lower ceteris paribus if the value of the initial business �V Ho;t�(yt�)

are higher; thus, the �rst condition only indicates that the return reversal (relative to the

investment-related anomalies) is less likely if the earnings from the current assets-in-place

are growing rapidly. Similarly, if the arrival and exercise of the growth option is very likely at

t�+1, then the value of the new business �V Hn;t�(�t�) will also be higher, and �H(t��1; t�+1)

will be higher, other things held �xed. Finally, if the exercise price of the future growth

options (In) is small relative to the ROG investment (FHn ); then the value of the �rm after

the ROG investment will be higher relative to the value prior to the ROG investment, and

�H(t� � 1; t� + 1) will be higher, other things held �xed.15

The second and third conditions in Proposition 4 are suggestive of large ROG investment

programs. In particular, the third condition suggests that the positive ROG investment-

return relation is more likely to occur if the new growth options generated by the ROG

investment are large in the sense of having high exercise price (In) � that is, requiring large

initial �nancing to develop the option. Similarly, the second condition is more likely to apply

to major innovations, such as new blockbuster drugs or product innovations that can create

new ecosystems (Adner, 2012). Finally, using the well known dynamic relation between book

asset growth and earnings growth, the �rst condition of the Proposition suggests that return-

reversals are more likely if ceteris paribus the asset growth prior to the ROG investment has

been slow.

15We reiterate that the conditions in Proposition 4 are su¢ cient and not necessary conditions; hence, anyof the conditions may be relaxed if the other conditions are su¢ ciently tightened. For example, condition(3) may be relaxed if the �rm�s current business is declining (that is, yt� � yt��1 < 0):

26

The su¢ cient conditions of Proposition 4 suggest that return-reversals from ROG in-

vestments are less likely for smaller �rms. This is because, in the presence of well known

frictions in external �nancing channels (Stiglitz and Weiss, 1983; Myers and Majluf, 1984),

such �rms may optimally choose not to undertake ROG investment programs that will gen-

erate growth options requiring large initial funding for development. Moreover, small �rms

that undertake ROG investments are often in the hi-tech sector and typically operate in a

constrained funding environment. Such �rms are, therefore, likely to choose R&D projects

with relatively high likelihood of success in a short time-frame.16 The following result shows

that the combination of the two aforementioned real option characteristics is su¢ cient to

rule out return-reversals even if the �rm has no current assets-in-place.

Corollary 2 Suppose �rst that the �rm is small in the sense that �V Ho;t = 0, t = 0; 1; 2:::

Then there exists �� > �� and � > 0 such that investment-return relation is negative, i.e.,

�H(t� � 1; t� + 1) > 0; if �t� � �� or�FHnIn

�� �:

Figures 5 and 6 present two simulations of the equilibrium rates of return of HIP �rms.

We highlight the di¤erence in pre- and post-ROG investment returns. Moreover, we simulate

returns for a few periods after the ROG but prior to the arrival of the innovation.

In Figure 5, there is a signi�cantly positive e¤ect of the ROG investment on equilibrium

returns, while Figure 6 depicts a negative relation between ROG investment and immediately

subsequent returns. A critical di¤erence in parametric assumptions underlying Figures 5 and

6 is that in the former the ratio of the future growth option investment (In) to the ROG

16For example, we do not typically observe small hi-tech �rms investing in developing new computerchip architectecture or small biopharmaceutical �rms investing in fundamental medical cures, because thelikelihood of achieving these breakthroughs in a short time span is very low.

27

investment (FHn ) is relatively high, namely,InFHn

= 257:5= 3:33; while in the latter this ratio is

InFHn

= 127:5= 1:6: Furthermore, in Figure 5, the probability of the arrival of the innovation is

low ( (�) = 0:22) compared with that assumed in Figure 6 ( (�) = 0:52): Hence, consistent

with Proposition 4, we tend to see a positive e¤ect of the ROG investment on immediately

subsequent returns, but this is not the case in Figure 6.

We note also that both Figures 5 and 6 show considerable return volatility after the ROG

investment and prior to the arrival of the innovation, the value of the ROG investment is

still driven by the random arrival of the signals f�t�+ig: Hence, return-reversals, namely,

up-ticks in returns are possible for many periods after the ROG investment event.

Meanwhile, the comparative statics of Propositions 2 and 4 above yield refutable predic-

tions on the determinants of the post-ROG investment stock returns that are empirically

testable with appropriate measures (or empirical proxies) of the investment potential of �rms.

We present these empirical tests in the next section.

4 Empirical Tests

We �rst motivate our empirical measures for capital investment and the proxy for innovation

potential. We next describe the data and sample selection, followed by the empirical testing

methodology and speci�cations. We then present and discuss the results.

4.1 Empirical Measures

Consistent with our theoretical model, we use growth in capital expenditure (IG) as the

empirical measure for investment. This measure has been used recently in empirical studies

28

of the investment-return relation (e.g., Xing, 2008). However, for robustness we also employ

the investment-to-capital ratio (IK), capital expenditure divided by lagged net PPE, as a

measure for investment; this measure has also been used recently in the literature (Polk

and Sapienza, 2009).17 Meanwhile, the level of R&D expenditures is the most widely used

proxy for �rms�innovative e¤ort (see, e.g., Rogers, 1998). And while patent holdings and

technological property rights are also potential measures of innovation potential (Pakes,

1986), the majority of �rms on COMPUSTAT do not hold any patents. We, therefore,

use R&D intensity, namely the ratio of R&D expenditure to sales (RDS), as the proxy for

IP.18 Speci�cally, we classify �rms with non-missing RDS as high IP �rms, while �rms with

missing RDS are classi�ed as low IP �rms.

4.2 Data and Sample Selection

Since we focus on R&D expense in identifying ROG investment, our sample starts in 1976

to ensure the quality of R&D expense data. Prior to 1976, companies had more discre-

tion in deciding the coverage and reporting of R&D expenses. In particular, the accounting

treatment of R&D expense reporting was standardized in 1975 (Financial Accounting Stan-

dards Board Statement No. 2). Our sample is, therefore, from 1976 to 2011 and consists

of �rms at the intersection of COMPUSTAT, and CRSP (Center for Research in Security

Prices). We obtain accounting data from COMPUSTAT and stock returns data from CRSP.

All domestic common shares trading on NYSE, AMEX, and NASDAQ with accounting and

17While our model relates to optimal investment policy, some studies also examine empirically the relationof asset growth (AG, Cooper et al. 2008) and investment-to-assets (IA, Lyandres, Livdan, and Zhang, 2008)to subsequent stock returns. In untabulated results, we �nd similar results for AG and IA.18However, using patents-based measures instead of R&D intensity generates similar results, as do other

R&D-based measures, such as scaling R&D expenditures with assets.

29

returns data available are included except �nancial �rms, which have four-digit standard

industrial classi�cation (SIC) codes between 6000 and 6999 (�nance, insurance, and real

estate sectors).19

We note that capital expenditures (CAPX) in COMPUSTAT include costs of building

R&D labs/infrastructure, acquiring patents, and buying R&D equipment/inventory with

future usage. Hence, the CAPX measures for high RDS �rms should capture the ROG

capital investment that is the focus of our study.

4.3 Empirical Test Methodology

We note that Propositions 2 and 4 generate cross-sectional predictions on the e¤ects of

capital investments on future returns. That is, they identify determinants of the cross-

sectional heterogeneity in the investment-return dynamics. We, therefore, use cross-sectional

empirical tests.

We �rst form ten portfolios based on the capital investment measures (IG and IK).

Speci�cally, at the end of June of each year t from 1977 to 2011, we sort �rms into ten

investment portfolios based on the investment measures in �scal year ending in calendar

year (t � 1). To form the two IP groups, we assign �rms with missing R&D expenditure

scaled by sales (RDS) in �scal year ending in calendar year (t�1) to the low IP group and the

rest to the high IP group. As noted above, the reporting of R&D expenses was standardized

19Following Fama and French (1993), we exclude closed-end funds, trusts, American Depository Receipts,Real Estate Investment Trusts, units of bene�cial interest, and �rms with negative book value of equity. Tomitigate back�lling bias, we require �rms to be listed on Compustat for at least two years. And, followingFama and French (2006), we also exclude �rms with total assets below $25 million to reduce the in�uenceof very small �rms. However, untabulated results indicate that including these very small �rms generatessimilar results.

30

in 1975. Hence, it is reasonable to assume that missing R&D expenditure in our sample

period is equivalent to zero R&D expenditure. However, assigning �rms with zero RDS to

the low IP group generates similar results. Furthermore, alternative R&D intensity measures

(e.g. R&D/assets) also generate similar results.

To test the predictions of Propositions 2 and 4, we then use Fama and MacBeth (1973)

(FM) cross-sectional regressions of individual stocks�returns in each of the �ve post-sorting

years (Year 1 to Year 5) on a set of independent variables that include (separately) the

decile-ranked investment measures and their interaction with the variables identi�ed in the

theoretical results. However, results using the raw values of capital investment are very

similar. In addition, we control for size, BTM, and momentum (measured by the cumula-

tive returns over the prior 11 months with a one-month gap). Speci�cally, for testing the

predictions of Proposition 2 we use the regression speci�cation for �rm j and dates t + i;

i = 1; 2; :::; 5 (where t is the investment date):

Rj;t+i = aj + b0jMjt+i + cjRIGjt + djLIPjt + ej(RIGjt � LIPjt � �jt) + �j;t+i (31)

where,Mjt+i is a vector of control variables (at date t+ i); RIGjt = 0; :::9 is the decile rank

of the �rm�s IG at t; LIPjt is an indicator variable that takes a value of 1 if the �rm was

a low IP �rm at t (and 0 otherwise), �jt is an independent variable that is implicated by

Proposition 2, and �j;t+i is an error term. The speci�cation is also re-estimated using IK

instead of IG as the investment measure. Finally, the speci�cation for testing the predictions

of Proposition 4 is analogous, where we use a dummy variable to identify high IP �rms.

31

4.4 Sample Descriptive Statistics

In Table 1, we present some descriptive statistics of our sample. We report the time-series

average of cross-sectional mean characteristics of the investment portfolios (for both IG and

IK) for the low RDS (or LIP) �rms and the high RDS (or HIP) �rms. For each investment

portfolio, we report the average investment, market capitalization (size), book-to-market

equity (BTM), beta (see below), lagged asset and sales growth, and the lagged return on

assets (ROA, namely, EBIT/Assets) and the asset turnover ratio (SA, namely, sales scaled

by assets).20

We note that the spread in investment is similar across low and high RDS �rms, suggesting

that the role played by R&D intensity in our results (see below) is not driven by di¤erences in

investment spread. Moreover, in both R&D-intensity groups, size has an inverted-U shaped

relation to investment, i.e., investment and size are positively correlated up to a medium level

of investment, following which they are negatively correlated. On the other hand, investment

and BTM are negatively correlated in both RDS groups.21 Meanwhile, in both RDS groups,

the relationship between investment and beta tends to be U-shaped, and similarly for the

relation between investment and lagged growth variables. Finally, the relationship between

investment and the lagged ROA (or SA) is non-monotonic in both RDS groups.

Overall, Table 1 indicates that the relation of investment � both IG and IK � to size,

BTM, and other independent variables implicated by Propositions 2 and Proposition 4, is

20Although we do not report the level of RDS in Table 1, by construction, low RDS �rms have missing RDS,while high RDS �rms are R&D active. For example, the average RDS of the ten IG portfolios ranges from11.20% to 56.45% in the high RDS �rms. To reduce the in�uence of outliers, we winsorize all characteristicsat the top and bottom 1%.21But, as noted above, our empirical tests will control for size and BTM.

32

similar across the two R&D intensity groups. We now report and discuss the results of our

empirical analysis.

4.5 Results

4.5.1 Tests on LIP Firms

In this section, we present and discuss the empirical tests of the predictions regarding the

investment-return dynamics of LIP �rms that are given in Proposition 2.

Table 2 reports the time-series average slopes, intercepts (in percentage), and their time-

series t-statistics (in parentheses) from monthly FM cross-sectional regressions (for the spec-

i�cation (31)) when, consistent with the model, we proxy the sales/earnings state variable xt

by the ROA (Panel A) and the asset turnover ratio (Panel B) in the year immediately prior

to the investment. Complementing the results in the literature, higher capital investment

ceteris paribus has a signi�cantly negative in�uence on returns in the �rst post-investment

year among LIP �rms. These e¤ects are also economically signi�cant. For example, Panel

A1 indicates that a one decile increase in the IG rank lowers the average monthly return in

the year after investment by 0.05%, other things held �xed, among LIP �rms; and Panel

A2 shows similar magnitude for IK. The regression results also con�rm the well-known size,

BTM, and momentum e¤ects on cross-sectional stock returns.

The novel aspect of the results in Table 2 are with respect to the interaction of R&D

intensity � the proxy for �rm innovation potential � and (lagged) ROA or asset turnover

with the e¤ects of capital investments, captured by the estimates for the interaction terms.

These results show that, within the LIP group of �rms, the negative investment-return

33

relation is moderated (or is less negative) for �rms that had higher ROA or asset turnover

prior to the capital investment. The moderating in�uence of lagged ROA and asset turnover

is statistically signi�cant for both measures of capital investment, and the magnitude of the

ROA e¤ect is also large. Thus, these results support the prediction of Proposition 2 with

respect to the earnings/sales state variable.

In Table 3, Panel A, we analyze the e¤ects of the systemtic risk �x on the investment-

return dynamics of LIP �rms. According to Proposition 2, higher systematic risk �rms

should have a more negative return response to capital investment, if this investment is

su¢ ciently large. We, therefore, do a four-way interaction, where we also control for the

size of the capital investment. Here, we use the �rm�s market beta with respect to the

CRSP value-weighted index as a proxy for �x: We �rst estimate monthly market beta by

regressing stock returns over the prior 60 months (with a minimum of 12 months) on market

returns. We then compute the average monthly beta in year (t � 1). We control for the

size of the investment by the dummy variable, High IG (or High IK), which equals 1 if

a �rm�s IG (or IK) is above the median level. Consistent with the theoretical prediction,

higher systematic risk �rms with relative large capital investments ceteris paribus exhibit

greater negative investment-return dynamics. We note that the slope is very small for the

IG measure, because this measure does not adjust for the asset size, since it is simply the

growth in capital expenditures. However, when we use the asset-adjusted measure of capital

investment (IK), the slope is discernible and statistically signi�cant.

Finally, empirical tests of the comparative statics with respect to the investment costs

FL are challenging because there are no readily available consensus estimates of �rm-speci�c

34

capital and capital adjustment costs. However, we use use the industry-speci�c estimates

of capital adjustment costs provided by Hall (2004), and the results are shown in Panel B

of Table 3. Thus, HAC (high adjustment costs) is a dummy variable that �ags �rms in

industries that have above-median estimated adjustment costs in Hall (2004). Speci�cally,

HAC equals 1 if a �rm operates in industries with high adjustment costs de�ned as Fama and

French (1997) industries 19 (steel) and 28 (mining), transportation equipment (2-digit SIC

code 37), and measuring instruments (2-digit SIC code 38). Consistent with Proposition 2,

�rms in HAC industries ceteris paribus exhibit signi�cantly more negative e¤ects of capital

investment on stock returns.22

4.5.2 Tests on HIP Firms

In this section, we present and discuss the empirical tests of the predictions in Proposition

4 regarding the investment-return dynamics of HIP, namely, the high RDS �rms.

Table 4 shows the e¤ects of lagged growth in assets (Panel A) and lagged growth in

sales (Panel B). We note �rst that the HIP �rms have signi�cantly greater returns compared

with LIP �rms in all 5 post-investment years, for both measures of capital investment.

This is consistent with the view that capital investment by HIP �rms is more likely to

represent ROG investment, as argued above. Next, the growth in book earnings (yi�yi�1) is

positively related to the growth of book assets, other things held �xed. Thus, consistent with

Proposition 4, the returns in the year following investment are signi�cantly and negatively

related to the lagged asset growth � that is, the likelihood of return-reversals is low if the

22In Panel B of Table 3, we drop LRDS from the model since LRDS and HAC are positively correlated �that is, the high HAC industries (such as steel, mining, and transportation equipment) are also industrieswhere a high proportion of �rms fall in the LRDS category.

35

earnings growth prior to the ROG investment was high; however, the e¤ects of lagged sales

growth are of the right sign but less signi�cant.

Proposition 4 also relates the likelihood of return-reversals to the development costs and

the immediate arrival likelihood of the real options generated by the capital investment.

As we noted in the discussion that followed the Proposition, these conditions suggest that

return-reversals are more likely for capital investments by large HIP �rms. Table 5 (Panel

A) tests this hypothesis through the interaction term, IG*HIP*Big, where Big is a dummy

variable that identi�es �rms with size above the NYSE median size breakpoint. We �nd

that post-investment returns by HIP �rms are signi�cantly and positively related to �rm

size, as noted also by Kumar and Li (2013). Furthermore, in Panel B, we present the

e¤ects of capital investments on subsequent returns by HIP �rms in high development cost

(HDC) industries, namely, biopharmaceuticals, natural resources, and telecommunication

industries. Speci�cally, HDC is a dummy that equals 1 if a �rm operates in the following

industries based on Fama-French 48 industry classi�cations: 12 (medical equipment), and

13 (pharmaceutical products), 27 (precious metals), 28 (mining), 30 (oil and natural gas),

32 (telecommunications). Here we also �nd results that support the prediction that return-

reversals are more likely ceteris paribus when the investments generate real options that

require relatively high development costs.

5 Summary and Conclusions

In traditional or technologically mature industries, capital investments typically re�ect con-

version of available growth options � such as expansion options by �rms with stable market

36

power � to assets-in-place. However, in many industries � such as the technologically

driven real options-intensive industries � �rms can pro-actively improve the likelihood of

generating future growth options, for example by investing in long-range research facilities

and acquiring patents. Unlike investments that convert existing growth options to assets-

in-place, which have been typically considered in the existing real options literature, the

real-option generating capital investments (ROG investments) need not have negative ef-

fects on subsequent stock returns.

An equilibrium analysis of ROG capital investments, where �rms optimally invest to

create the capacity for stochastically generating future growth options, clari�es the conditions

under which such investment can raise expected returns or systematic risk. These conditions

are essentially that the generated real options be such that: (1) the investment required

to exercise the new growth options (when they arrive) are high relative to the initial ROG

investment and (2) the probability of the arrival and exercise of growth options immediately

after the ROG investment is not too high. These conditions will typically be satis�ed in cases

where the ROG investment is designed to develop relatively large innovation programs. In

addition, ROG investments undertaken by �rms with slowing growth in their existing lines

of business are ceteris paribus more likely to raise expected returns relative to the expected

returns preceding the investment.

The analysis above presents novel testable predictions that relate observable �rm char-

acteristics to both positive and negative e¤ects of capital investments on stock returns. We

empirically test these predictions using capital investments by high R&D intensity �rms to

identify ROG investments. Using a comprehensive sample of �rms from 1976-2011, and cross-

37

sectional Fama and Macbeth (1973) regressions, we �nd support for the main predictions of

the model.

The existing empirical literature largely documents a signi�cantly negative cross-sectional

relation between �rms�capital investments and subsequent stock returns. Our analysis ex-

tends this literature by providing a theoretical foundation for and new empirical evidence

on the signi�cant cross-sectional heterogeneity in the relation of capital investment to sub-

sequent stock returns.

38

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43

Appendix

Derivation of Equation (15): We establish the formula by induction. For s = t+ 1 :

E��Lmt+1

mt

exp(xt+1 ��2x2� �L) xt

�= �LEt

�exp(�r � �

2m

2� "m;t+1 + xt + "x;t+1 �

�2x2� �L)

�= �L

�exp(�(r + �x) + xt � �L)

�(32)

where the last expression in (32) follows from the maintained assumptions. For s = t +

2;under our maintained assumptions, we get:

E��2Lmt+2

mt

exp(xt+1 ��2x2� �L) xt

�(33)

= �2LEt�mt+1

mt

Et+1(mt+2

mt+1

exp(xt+1 + "x;t+1 ��2x2� �L)

�= �2LEt

�mt+1

mt

exp(�(r + �x) + xt+1 � �L)�

The last expression in (33) is:

�2L exp(�(r + �x)Et�exp(�r � �

2m

2� "m;t+1 + xt + "x;t+1 �

�2x2� �L)

�(34)

= �2L�exp(�2(r + �x) + xt � �L)

�

Forward induction on s = t+ 3; :::; and inserting in (14) then establishes (15).

44

Proof of Proposition 1: Using an argument similar to (15) and (16), we get:

V Lh;t+1(xt+1)� FL = GL(Kh)�L exp(xt+1 � �L)� FL (35)

From (35), we �nd that Et[mt+1

mt(V Lh;t+1(xt+1) xt+1 � x� ] is proportional to:

1Z(x��xt)

1Z�1

exp(�r � �2m

2� "m;t+1 + xt + "x;t+1 �

�2x2� �L)�("m;t+1; "x;t+1)d"m;t+1d"x;t+1 (36)

where �("m;t+1; "x;t+1) is the bivariate normal density with moments described above. But

noting that �("m;t+1; "x;t+1) = �("m;t+1; "x;t+1)�("x;t+1), where �("m;t+1; "x;t+1) is normal

with mean �x�2x"x;t+1 and variance �2m(1�

�2x�2x�

2m), we have,

1Z�1

exp(�r � �2m

2� "m;t+1 + xt + "x;t+1 �

�2x2� �L)�("m;t+1; "x;t+1)d"m;t+1

= exp

��r � �2x

2�2x+ xt + "x;t+1(1�

�x�2x)� �

2x

2� �L

�(37)

Hence, using (37), we can write (36) as:

exp

��r � �2x

2�2x+ xt �

�2x2� �L

� 1Z(x��xt)

exp

�"x;t+1(1�

�x�2x)

��("x;t+1)d"x;t+1 (38)

But we can compute the integral in (38) as (see, e.g., Norgaard and Killeen, 1980),

1Z(x��xt)

exp

�"x;t+1(1�

�x�2x)

��("x;t+1)d"x;t+1 = exp

��2x2(1� �x

�2x)2��1� ��(x

� � xt�x

)

�(39)

45

where ��(�) is the standard normal cdf. Inserting(39) in (38) and using (36)- (37), we obtain:

Et[mt+1

mt

(V Lh;t+1(xt+1) xt+1 � x� ] = exp��(r + �x) + xt � �L

� �1� ��(x

� � xt�x

)

�(40)

Meanwhile,

Et[mt+1

mt

FL xt+1 � x� ] = (1� ��(x� � xt�x

))FLe�r (41)

Finally, we note that because xt+1 = xt + "x;t+1;�(x� xt) = ��(x

��xt�x

): The computation

of Et[mt+1

mt(V L`;t+1(xt+1) xt+1 < x� ] given in the Proposition then follows analogous to the

derivation given above. Q.E.D

Proof of Proposition 2: Recall that �L(t��1; t�+1) � Et��1[RLt��1;t� ]�Et� [RLt�;t�+1]:

We then compute:

@�L(t� � 1; t� + 1)@FL

/ (1� �(x� xt))(e�x � 1)[ �V Lt (xt) + FLe�r] > 0 (42)

Turning, next, to the comparative statics with respect to xt, we note that@�(x� xt)

@xt< 0

because of �rst order stochastic dominance. Hence,

@�L(t� � 1; t� + 1)@xt

/ FL(e�x � 1)"fexp(xt � �L � (r + �x))DL(x� xt)[

@�(x� xt)

@xt�

(1� �(x� xt)]g � FLe�r(1� �(x� xt))@�(x� xt)

@xt

#(43)

Hence, @�L(t��1;t�+1)

@xt< 0 if exp(xt � �L � (r+ �x))DL(x� xt) � FLe�r(1��(x� xt)); which

is true since �V Lt (xt) � 0 (cf. Proposition (1)). Finally, we can compute

46

@�L(t� � 1; t� + 1)@�x

/ FL(1� �(x� xt))h�V Lt (xt)e

�x + (e�x � 1)e(xt��L�(r+�x))DL(x�)i+

@�L(t� � 1; t� + 1)@x�

@x�

@�x(44)

But,

@�L(t� � 1; t� + 1)@x�

/ �FL(e�x � 1)e(xt��L�(r+�x))hDL(x� xt)�(x

� xt)+

+@DL(x� xt)

@x�(1� �(x� xt))]

#@x�

@�x/ �

�FL

�L[GL(Kh)�GL(K`)]

��1@�L@�x

> 0 (45)

However, from Proposition (1),

DL(x� xt)�(x� xt) +

@DL(x� xt)

@x�(1� �(x� xt)) = �L�(x� xt)GL(K`) > 0 (46)

(44)-(46) imply that @�L(t��1;t�+1)

@�x> 0 if

DL(x� xt)(1� �(x� xt) >��(x� xt)G

L(K`)�� FL

[GL(Kh)�GL(K`)]

��1@�L@�x

(47)

But the L.H.S of (47) is increasing in GL(Kh) � GL(K`) while the R.H.S is decreasing in

this quantity. Q.E.D.

Proof of Proposition 4: For notational convenience, put Hn = Hn � (1���(��))FHn :

47

Note that �H(t� � 1; t� + 1) < 0 if

�exp(yt� � �Ho )GHo �H;o + �Hn;t�(�t�)

��V Ht��1(yt��1) >

�V Ht� (yt� ; �t�)[exp(yt��1 � �Ho )GHo �H;o + Hn ]

(48)

Then, noting that:

exp(yi � �Ho )GHo (Qo)�H;o = e(r+�y) �Vo;i(yi)

�V Ht��1(yt��1) = �V Ho;t��1(yt��1) +�V Ht��1

�V Ht� (yt� ; �t�) = �V Ho;t�(yt�) + �V Hn;t�(�t�)

(48) simpli�es to:

�V Ho;t��1[�Hn;t� � �V Hn;t�e

(r+�y)] + �V Ho;t� [ �VHn;t��1e

(r+�y) � Hn ] > �V Hn;t�Hn � �Hn;t� �V Hn;t��1 (49)

(Here, we suppress the dependence on the variables on their respective state variables for

notational ease.) Now, for convenience, put

A0(��; z�) = E[(1� �z(z� �)) � � ��]

A1(��; z�) = E[(1� �z(z� �)) exp(�z + ��� �Hn ) � � ��]

48

We then compute (for �z = �y = �):

�Hn;t� � �V Hn;t�e(r+�) = (1� �z(z� �t�))In[e� � 1] (50)

�V Hn;t��1e(r+�) � Hn = [1� e�]f(1� ��(��))FHn + InA0(��; z�)g (51)

�V Hn;t�Hn � �Hn;t� �V Hn;t��1 = [1� e��] (1� �z(z� �t�))GHn �Hn e�r �

( InA0 + (1� ��(��))FHn ) exp(�z + ��t� � �Hn )� InA1

(52)

Using these, (49) can be written as:

(1� �z(z� �t�))h�V Ho;t��1 + e

�(A1t� � A0 �V Hn;t�)i� �V Ho;t�A0

>

�FHn (1� ��(��)

In

�h e�(1� �z(z� �t�) �V Hn;t� + �V Ho;t�

i(53)

where A1t� = E[(1� �z(z� �)) �V Hn;t�(�) � � ��]: Now, the LHS of (53) is strictly positive if

E[(1� �z(z� �)) exp(�z + ��� �Hn ) � � ��]� A0 exp(�z + ��t� � �Hn ) >

[(1� �z(z� �t�) e(r+�+�Ho )]�1

�GHo �

Ho

GHn �Hn

�hexp(yt�)A0 � exp(yt��1)(1� �z(z� �t�))

i(54)

But (1 � �z(z� �)) exp(�z + �� � �Hn ) is an increasing function of � because@�z(z� �)

@�< 0

from strict �rst order dominance. Moreover, because A0(��; z�) is a given number the LHS

49

of (54) is strictly positive at �t� = ��, so that there is some a such that:

E[(1� �z(z� �)) exp(�z + ��� �Hn ) � � ��]� A0 exp(�z + ��� � �Hn ) � a > 0

Hence, from continuity, for any �t� � �� su¢ ciently small there exists �y > 0 such that (54)

holds if yt� � yt��1 � �y: But then (53) is satis�ed if (54) holds and�FHnIn

�is su¢ ciently

small. Q.E.D.

Proof of Corollary 2: Suppose �V Ho;t = 0: Then (53) specializes to:

(1� �z(z� �t�)) e�(A1t� � A0 �V Hn;t�) >(1� ��(��))FHn

In(1� �z(z� �t�)e�r �V Hn;t�

Now there exists a �� such that A1t� � A0 �V Hn;t� < 0 for any �t� � ��: Hence, (53) is not

feasible if �t� � �� and �V Ho;t = 0: Q.E.D.

50

Date t Date s � t+1 Date � � s

ROG investment Innovation Innovation(FHn ) arrives exercised

(In)

Figure 1: Sequence of events

51

52

Figure 2 simulates the equilibrium returns of the low innovation potential firm that optimally

times capital investment to exercise its capacity expansion option. Here, GL(K) = K

0.5. The other

parameters are (x= 0.08, x = 0.2, L= 0, F

L = 5, K

H = 100, K

L = 50, X0 = -2.25, r = 0.036,

L).

0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.135

0.14

0.145

Rat

es

of

Re

turn

Time

Returns of LIP Firms

53

Figure 3 simulates the equilibrium returns of the low innovation potential firm that optimally

times capital investment to exercise its capacity expansion option. Here, GL(K) = K

0.5. The other

parameters are (x= 0.08, x = 0.2, L= 0, F

L = 5, K

H = 150, K

L = 50, X0 = -2.25, r = 0.036,

L).

0.11

0.115

0.12

0.125

0.13

0.135

0.14

0.145

0.15

Rat

e o

f R

etu

rn

Time

Returns of LIP Firms

54

Figure 4 simulates the equilibrium returns of the low innovation potential firm that optimally

times capital investment to exercise its capacity expansion option. Here, GL(K) = K

0.5. The other

parameters are (x= 0.08, x = 0.2, L= 0, F

L = 5, K

H = 200, K

L = 50, X0 = -2.25, r = 0.036,

L).

0.115

0.12

0.125

0.13

0.135

Rat

es

of

Re

turn

Time

Returns of LIP Firms

55

Figure 5 simulates the equilibrium returns of the high innovation potential firm that optimally

times its real option generation (ROG) capital investment. The equilibrium returns prior to the

ROG investment are shown in blue while those immediately after that investment (but prior to

the arrival of the innovation) are shown in red. Here, GH

o (K) = K

0.5, G

Hn

(K) = K

0.75. The

parameters are (y= z = 0.08, y = 0.2, z = 0.3, = 0.2, z = -1.5, H=

L = 0, F

Hn

= 7.5,

Qo = 50, r = 0.036,

o

nQn = 20, n).

0.115

0.12

0.125

0.13

0.135

0.14

0.145

Rat

e o

f R

etu

rn

Time

Returns of HIP Firms

56

Figure 6 simulates the equilibrium returns of the high innovation potential firm that optimally

times its real option generation (ROG) capital investment. The equilibrium returns prior to the

ROG investment are shown in blue while those immediately after that investment (but prior to

the arrival of the innovation) are shown in red. Here, GH

o (K) = K

0.5, G

Hn (K) = K

0.75. The

parameters are (y= z = 0.12, y = 0.2, z = 0.4, = 0.4, z = 0.5, H=

L = 0, F

Hn

= 7.5,

Qo = 50, r = 0.036,

o

n Qn = 10, n).

0.11

0.13

0.15

0.17

0.19

0.21

0.23

Rat

e o

f R

etu

rn

Time

Returns of HIP Firms

57

Table 1. Summary statistics

At the end of June of each year t from 1977 to 2011, we sort firms independently into ten investment portfolios

based on investment measures in fiscal year ending in calendar year t – 1. We use two investment measures: growth

in capital expenditure (IG), and investment-to-capital ratio (IK) computed as capital expenditure divided by lagged

net PPE. We assign firms with missing R&D expenditure scaled by sales (RDS) in year t – 1 to the low RDS group

and the rest to the high RDS group. For each portfolio, we report the time-series mean of cross-sectional average

characteristics. Ln(Size) is the natural log of market capitalization in millions. Ln(BTM) is the natural log of book-

to-market equity. To compute firms’ market beta, we first estimate monthly market beta by regressing stock returns

over the prior 60 months (with a minimum of 12 months) on market returns (CRSP value-weighted index). We then

compute the average monthly beta in the same year. Lag(AG) denotes asset growth measured in the fiscal year

ending in calendar year t – 2. Lag(ROA) is return-on-assets measured by income before extraordinary items scaled

by total assets measured in the fiscal year ending in calendar year t – 2. Lag(SA) denotes sales-to-assets ratio

measured in the fiscal year ending in calendar year t – 2. Lag(SG) denotes sales growth measured in the fiscal year

ending in calendar year t – 2. IG, IK, BTM, and market beta are measured in the fiscal year ending in calendar year

t – 1. Size is measured at the end of June in year t. All variables are winsorized at the top and bottom 1%. Financial

firms and firms with assets below $25 million are excluded.

Panel A. Investment = IG

RDS rank IG rank Firm No. IG ln(Size) ln(BTM) Beta Lag(AG) Lag(ROA) Lag(SA) Lag(SG)

Low 1 (Low) 141 -0.67 4.24 -0.10 1.14 0.15 -0.01 1.20 0.14

2 133 -0.39 4.90 -0.16 1.06 0.14 0.02 1.27 0.14

3 136 -0.22 5.32 -0.21 1.02 0.13 0.03 1.23 0.13

4 138 -0.09 5.66 -0.24 0.97 0.13 0.04 1.17 0.14

5 138 0.03 5.82 -0.29 0.95 0.13 0.04 1.16 0.14

6 138 0.16 5.83 -0.32 0.96 0.15 0.04 1.18 0.16

7 139 0.31 5.68 -0.37 1.00 0.17 0.04 1.23 0.17

8 135 0.54 5.45 -0.39 1.06 0.20 0.04 1.29 0.19

9 136 0.98 5.18 -0.41 1.10 0.22 0.04 1.27 0.23

10 (High) 139 3.28 4.65 -0.45 1.18 0.29 0.02 1.23 0.27

High 1 (Low) 151 -0.66 4.36 -0.33 1.45 0.12 -0.06 1.16 0.16

2 160 -0.39 5.01 -0.38 1.33 0.13 0.00 1.26 0.16

3 157 -0.22 5.50 -0.44 1.27 0.14 0.02 1.28 0.15

4 154 -0.09 5.79 -0.50 1.23 0.14 0.03 1.32 0.15

5 154 0.03 6.08 -0.54 1.22 0.14 0.04 1.29 0.14

6 154 0.16 6.06 -0.57 1.24 0.16 0.04 1.32 0.16

7 154 0.31 5.83 -0.58 1.27 0.17 0.04 1.33 0.17

8 158 0.54 5.59 -0.63 1.31 0.21 0.04 1.35 0.20

9 156 0.98 5.31 -0.69 1.39 0.26 0.04 1.29 0.25

10 (High) 153 3.08 4.82 -0.74 1.53 0.35 0.00 1.17 0.31

58

Panel B. Investment = IK

RDS rank IK rank Firm No. IK ln(Size) ln(BTM) Beta Lag(AG) Lag(ROA) Lag(SA) Lag(SG)

Low 1 (Low) 185 0.05 4.80 0.04 0.96 0.07 -0.01 0.88 0.09

2 174 0.09 5.40 -0.09 0.87 0.09 0.02 1.02 0.10

3 151 0.13 5.46 -0.14 0.92 0.11 0.03 1.11 0.11

4 138 0.16 5.51 -0.24 0.98 0.14 0.03 1.21 0.14

5 126 0.20 5.46 -0.30 1.02 0.15 0.04 1.31 0.16

6 126 0.25 5.45 -0.35 1.06 0.18 0.04 1.40 0.18

7 128 0.31 5.36 -0.41 1.12 0.19 0.05 1.44 0.19

8 124 0.40 5.30 -0.49 1.16 0.23 0.05 1.43 0.22

9 121 0.55 5.18 -0.57 1.22 0.29 0.05 1.41 0.28

10 (High) 113 1.26 4.86 -0.71 1.31 0.44 0.04 1.25 0.39

High 1 (Low) 108 0.05 4.23 -0.13 1.26 0.04 -0.06 1.14 0.10

2 121 0.10 5.00 -0.24 1.19 0.06 -0.01 1.23 0.08

3 144 0.13 5.50 -0.33 1.17 0.10 0.01 1.26 0.10

4 157 0.16 5.69 -0.40 1.15 0.11 0.02 1.31 0.11

5 168 0.20 5.79 -0.46 1.19 0.12 0.03 1.32 0.13

6 168 0.25 5.78 -0.52 1.24 0.14 0.03 1.34 0.15

7 167 0.31 5.72 -0.59 1.30 0.17 0.03 1.36 0.17

8 170 0.40 5.52 -0.67 1.38 0.23 0.04 1.35 0.22

9 174 0.56 5.35 -0.77 1.52 0.29 0.04 1.30 0.29

10 (High) 181 1.24 5.23 -0.96 1.72 0.51 0.02 1.11 0.46

59

Table 2. Interaction of investment with lagged earnings state proxies for LIP firms

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in

parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in

each of the five post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t

to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June

of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t

+ 5. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal

year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Ln(Size) is the natural logarithm

of market equity at the beginning of each period. Momentum is the cumulative return over the prior 11 months with

a one-month gap. We proxy earnings state prior to investment with return-on-assets (net income/assets, ROA) and

sales-to-assets ratio in fiscal year ending in calendar year t – 2 in Panels A and B, respectively. We use two

investment measures: growth in capital expenditure (IG), and investment-to-capital ratio (IK) computed as capital

expenditure divided by lagged net PPE. Investment measures are the deciles rank of investment measured in the

fiscal year ending in calendar year t – 1 ranging from 0 to 9. LRDS is a dummy variable that equals 1 if a firm’s

R&D expenditure scaled by sales in year t – 1 is missing. All independent variables (except rank variables and

dummies) are winsorized at the top and bottom 1%. Financial firms and firms with assets below $25 million are

excluded. The sample period for stock returns is from July of 1977 to December 2011.

Panel A. Earnings state proxy = ROA

Panel A1. Investment = IG

Year IG IG*LRDS*Lag(ROA) LRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.05 0.31 -0.33 -0.09 0.25 0.57 1.98

(-5.07) (4.08) (-3.73) (-1.94) (3.23) (2.58) (4.48)

2 -0.01 0.09 -0.28 -0.12 0.13 0.49 1.94

(-0.66) (1.13) (-3.00) (-2.46) (1.73) (2.17) (4.35)

3 0.00 0.12 -0.21 -0.13 0.04 0.45 1.94

(-0.47) (1.35) (-2.36) (-2.75) (0.52) (1.99) (4.52)

4 -0.01 0.04 -0.20 -0.14 -0.02 0.30 2.03

(-1.54) (0.39) (-2.23) (-3.00) (-0.29) (1.30) (4.70)

5 0.00 0.07 -0.24 -0.12 0.01 0.26 1.89

(-0.45) (0.70) (-2.54) (-2.68) (0.13) (1.09) (4.36)

Panel A2. Investment = IK

Year IK IK*LRDS*Lag(ROA) LRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.03 0.25 -0.35 -0.09 0.23 0.59 1.94

(-1.99) (3.31) (-4.15) (-2.02) (3.45) (2.71) (4.83)

2 0.00 0.10 -0.28 -0.12 0.13 0.49 1.90

(0.09) (1.20) (-3.15) (-2.48) (2.00) (2.20) (4.68)

3 0.00 0.07 -0.21 -0.13 0.02 0.45 1.94

(-0.31) (0.82) (-2.51) (-2.81) (0.36) (2.00) (4.92)

4 0.00 0.07 -0.22 -0.14 -0.01 0.30 1.99

(-0.20) (0.67) (-2.55) (-3.00) (-0.19) (1.29) (4.93)

5 0.01 -0.03 -0.21 -0.12 0.02 0.27 1.83

(0.39) (-0.25) (-2.46) (-2.67) (0.27) (1.13) (4.59)

60

Panel B. Earnings state proxy = Sales/Assets

Panel B1. Investment = IG

Year IG IG*LRDS*Lag(Sales/Assets) LRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.06 0.03 -0.44 -0.08 0.25 0.56 1.97

(-5.63) (4.26) (-4.13) (-1.65) (3.28) (2.54) (4.41)

2 -0.01 0.01 -0.31 -0.11 0.13 0.48 1.94

(-1.03) (1.27) (-2.86) (-2.37) (1.74) (2.15) (4.31)

3 -0.01 0.01 -0.22 -0.13 0.03 0.44 1.92

(-0.58) (0.81) (-2.10) (-2.65) (0.40) (1.96) (4.45)

4 -0.02 0.00 -0.22 -0.14 -0.02 0.30 2.03

(-1.81) (0.54) (-2.08) (-2.93) (-0.31) (1.29) (4.66)

5 -0.01 0.00 -0.25 -0.12 0.01 0.27 1.88

(-0.58) (0.50) (-2.22) (-2.62) (0.12) (1.11) (4.29)

Panel B2. Investment = IK

Year IK IK*LRDS*Lag(Sales/Assets) LRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.04 0.02 -0.44 -0.08 0.23 0.58 1.94

(-2.46) (3.37) (-4.59) (-1.80) (3.42) (2.66) (4.79)

2 0.00 0.01 -0.30 -0.11 0.12 0.48 1.90

(-0.15) (1.00) (-3.08) (-2.39) (1.96) (2.16) (4.66)

3 -0.01 0.01 -0.22 -0.13 0.01 0.43 1.94

(-0.45) (0.67) (-2.35) (-2.71) (0.22) (1.95) (4.88)

4 -0.01 0.00 -0.23 -0.14 -0.02 0.29 1.98

(-0.37) (0.49) (-2.37) (-2.91) (-0.31) (1.26) (4.89)

5 0.01 0.00 -0.21 -0.12 0.01 0.27 1.83

(0.33) (-0.28) (-2.05) (-2.63) (0.22) (1.13) (4.54)

61

Table 3. Interaction of investment with market beta and adjustment costs for LIP firms

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in

parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in

each of the five post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t

to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June

of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t

+ 5. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal

year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Ln(Size) is the natural logarithm

of market equity at the beginning of each period. Momentum is the cumulative return over the prior 11 months with

a one-month gap. Panel A reports the interaction with market beta. We use two investment measures: growth in

capital expenditure (IG), and investment-to-capital ratio (IK) computed as capital expenditure divided by lagged net

PPE. We first estimate monthly market beta by regressing stock returns over the prior 60 months (with a minimum

of 12 months) on market returns (CRSP value-weighted index). We then compute the average monthly beta in year t

– 1. Panel B reports the interaction with adjustment costs. High IG (High IK) is a dummy variable that equals 1 if a

firm’s IG (IK) in fiscal year ending in calendar year t – 1 is above the median level. HAC is a dummy variable that

equals 1 if a firm operates in industries with high adjustment costs defined as Fama and French (1997) industries 19

(steel) and 28 (mining), transportation equipment (2-digit SIC code 37), and measuring instruments (2-digit SIC

code 38). Investment measures are the deciles rank of investment measured in the fiscal year ending in calendar year

t – 1 ranging from 0 to 9. LRDS is a dummy variable that equals 1 if a firm’s R&D expenditure scaled by sales in

year t – 1 is missing. All independent variables (except rank variables and dummies) are winsorized at the top and

bottom 1%. Financial firms and firms with assets below $25 million are excluded. The sample period for stock

returns is from July of 1977 to December 2011.

Panel A. Interaction with market beta

Panel A1. Investment = IG

Year IG IG*LRDS*Beta*High IG LRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.04 0.00 -0.27 -0.09 0.24 0.58 1.92

(-4.07) (-0.19) (-2.42) (-1.83) (3.18) (2.61) (4.19)

2 0.00 0.00 -0.24 -0.12 0.12 0.49 1.92

(-0.17) (-0.49) (-2.11) (-2.47) (1.61) (2.21) (4.16)

3 0.01 -0.01 -0.14 -0.13 0.03 0.45 1.89

(0.63) (-1.18) (-1.33) (-2.74) (0.37) (2.00) (4.27)

4 -0.01 0.00 -0.18 -0.14 -0.02 0.31 2.02

(-1.01) (-0.56) (-1.67) (-3.02) (-0.34) (1.31) (4.52)

5 0.00 -0.01 -0.20 -0.12 0.01 0.26 1.87

(-0.05) (-0.88) (-1.83) (-2.68) (0.13) (1.09) (4.17)

Panel A2. Investment = IK

Year IK IK*LRDS*Beta*High IK LRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.01 -0.02 -0.23 -0.09 0.23 0.59 1.83

(-0.94) (-1.87) (-2.26) (-1.93) (3.36) (2.72) (4.38)

2 0.02 -0.02 -0.17 -0.12 0.12 0.49 1.83

(1.14) (-2.08) (-1.73) (-2.51) (1.84) (2.23) (4.36)

3 0.01 -0.01 -0.13 -0.13 0.01 0.45 1.89

(0.39) (-1.58) (-1.42) (-2.80) (0.24) (2.00) (4.63)

4 0.01 -0.01 -0.17 -0.14 -0.01 0.30 1.94

(0.39) (-1.23) (-1.75) (-2.99) (-0.23) (1.29) (4.68)

5 0.01 -0.01 -0.17 -0.12 0.02 0.27 1.80

(0.89) (-1.40) (-1.72) (-2.68) (0.35) (1.11) (4.36)

62

Panel B. Interaction with adjustment costs

Panel B1. Investment = IG

Year IG IG*LRDS*HAC ln(Size) ln(BTM) Momentum Intercept

1 -0.04 -0.06 -0.09 0.22 0.56 1.81

(-4.55) (-1.91) (-1.87) (2.64) (2.52) (4.32)

2 0.00 -0.05 -0.12 0.10 0.48 1.81

(-0.30) (-1.57) (-2.48) (1.24) (2.13) (4.29)

3 0.00 -0.05 -0.13 0.01 0.44 1.83

(0.04) (-1.63) (-2.72) (0.14) (1.93) (4.49)

4 -0.01 -0.06 -0.14 -0.04 0.29 1.93

(-1.49) (-1.95) (-2.96) (-0.48) (1.25) (4.72)

5 0.00 -0.06 -0.13 -0.02 0.25 1.78

(-0.32) (-1.64) (-2.69) (-0.25) (1.03) (4.33)

Panel B2. Investment = IK

Year IK IK*LRDS*HAC ln(Size) ln(BTM) Momentum Intercept

1 -0.02 -0.09 -0.09 0.21 0.59 1.73

(-1.16) (-2.22) (-1.95) (2.97) (2.67) (4.56)

2 0.01 -0.04 -0.12 0.11 0.49 1.75

(0.63) (-0.79) (-2.48) (1.60) (2.18) (4.57)

3 0.00 -0.05 -0.13 0.00 0.44 1.82

(0.11) (-1.26) (-2.78) (0.02) (1.96) (4.86)

4 0.00 -0.05 -0.14 -0.03 0.29 1.85

(0.23) (-1.02) (-2.94) (-0.40) (1.24) (4.86)

5 0.01 -0.07 -0.12 0.00 0.26 1.71

(0.70) (-1.22) (-2.69) (0.03) (1.08) (4.53)

63

Table 4. Interaction of investment with lagged asset growth and sales growth for HIP firms

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in

parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in

each of the five post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t

to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June

of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t

+ 5. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal

year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Ln(Size) is the natural logarithm

of market equity at the beginning of each period. Momentum is the cumulative return over the prior 11 months with

a one-month gap. We use two investment measures: growth in capital expenditure (IG), and investment-to-capital

ratio (IK) computed as capital expenditure divided by lagged net PPE. Investment measures are the deciles rank of

investment measured in the fiscal year ending in calendar year t – 1 ranging from 0 to 9. HRDS is a dummy variable

that equals 1 if a firm’s R&D expenditure scaled by sales in year t – 1 is non-missing. Panels A and B report the

interaction with asset growth and sales growth in year t – 2, respectively. All independent variables (except rank

variables and dummies) are winsorized at the top and bottom 1%. Financial firms and firms with assets below $25

million are excluded. The sample period for stock returns is from July of 1977 to December 2011.

Panel A. Interaction with asset growth

Panel A1. Investment = IG

Year IG IG*HRDS*Lag(Asset Growth) HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.02 -0.04 0.30 -0.09 0.19 0.50 1.65

(-3.03) (-2.39) (3.51) (-2.06) (2.63) (2.31) (4.25)

2 0.00 0.00 0.22 -0.12 0.08 0.47 1.70

(-0.03) (-0.17) (2.51) (-2.59) (1.10) (2.09) (4.33)

3 0.00 0.01 0.17 -0.13 0.02 0.40 1.74

(0.02) (0.66) (2.02) (-2.81) (0.33) (1.77) (4.59)

4 -0.01 -0.02 0.19 -0.13 -0.02 0.30 1.77

(-1.26) (-1.02) (2.26) (-2.80) (-0.36) (1.28) (4.61)

5 0.00 -0.01 0.21 -0.11 0.01 0.21 1.60

(0.23) (-0.70) (2.44) (-2.55) (0.21) (0.87) (4.21)

Panel A2. Investment = IK

Year IK IK*HRDS*Lag(Asset Growth) HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.01 -0.03 0.31 -0.10 0.19 0.53 1.60

(-0.75) (-1.80) (3.77) (-2.13) (2.91) (2.44) (4.42)

2 0.01 0.02 0.19 -0.12 0.09 0.48 1.66

(0.59) (1.34) (2.34) (-2.58) (1.45) (2.13) (4.58)

3 0.00 0.02 0.17 -0.13 0.02 0.41 1.74

(-0.09) (1.11) (2.04) (-2.83) (0.26) (1.80) (4.88)

4 0.00 -0.03 0.21 -0.13 -0.02 0.30 1.70

(0.26) (-1.73) (2.60) (-2.79) (-0.34) (1.27) (4.68)

5 0.01 0.00 0.20 -0.11 0.03 0.22 1.58

(0.64) (-0.22) (2.33) (-2.54) (0.52) (0.91) (4.37)

64

Panel B. Interaction with sales growth

Panel B1. Investment = IG

Year IG IG*HRDS*Lag(Sales Growth) HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.03 -0.03 0.28 -0.09 0.22 0.53 1.62

(-3.38) (-1.52) (3.34) (-1.90) (2.99) (2.41) (4.16)

2 0.00 -0.01 0.22 -0.11 0.10 0.47 1.67

(-0.48) (-0.73) (2.60) (-2.43) (1.49) (2.10) (4.26)

3 0.00 0.03 0.15 -0.12 0.04 0.41 1.73

(-0.47) (1.55) (1.77) (-2.69) (0.60) (1.78) (4.55)

4 -0.01 -0.01 0.18 -0.13 -0.02 0.31 1.79

(-1.89) (-0.42) (2.14) (-2.85) (-0.29) (1.31) (4.67)

5 0.00 0.01 0.21 -0.12 0.02 0.22 1.62

(-0.23) (0.58) (2.41) (-2.60) (0.31) (0.89) (4.24)

Panel B2. Investment = IK

Year IK IK*HRDS*Lag(Sales Growth) HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.02 -0.02 0.29 -0.09 0.21 0.55 1.57

(-1.16) (-1.11) (3.61) (-1.96) (3.25) (2.56) (4.35)

2 0.00 0.00 0.21 -0.11 0.11 0.48 1.63

(0.34) (0.16) (2.57) (-2.41) (1.84) (2.14) (4.46)

3 0.00 0.02 0.15 -0.12 0.03 0.41 1.72

(-0.17) (1.31) (1.90) (-2.71) (0.50) (1.81) (4.79)

4 0.00 -0.01 0.20 -0.13 -0.01 0.30 1.72

(-0.03) (-0.80) (2.42) (-2.85) (-0.24) (1.30) (4.74)

5 0.00 0.02 0.19 -0.11 0.03 0.22 1.60

(0.16) (0.94) (2.34) (-2.58) (0.52) (0.93) (4.42)

65

Table 5. Interaction of investment with size and development costs for HIP firms

This table reports the time-series average slopes and intercepts (in percentage) and their time-series t-statistics (in

parentheses) from monthly Fama and MacBeth (1973) cross-sectional regressions of individual stocks’ returns in

each of the five post-sorting years (Year 1 to Year 5) on a set of independent variables. Year 1 is from July of year t

to June of year t + 1. Year 2 is from July of year t + 1 to June of year t + 2. Year 3 is from July of year t + 2 to June

of year t + 3. Year 4 is from July of year t + 3 to June of year t + 4. Year 5 is from July of year t + 4 to June of year t

+ 5. Ln(BTM) denotes the natural logarithm of book-to-market equity (BTM), the ratio of book equity in the fiscal

year ending in calendar year t – 1 to market equity at the end of calendar year t – 1. Ln(Size) is the natural logarithm

of market equity at the beginning of each period. Momentum is the cumulative return over the prior 11 months with

a one-month gap. We use two investment measures: growth in capital expenditure (IG), and investment-to-capital

ratio (IK) computed as capital expenditure divided by lagged net PPE. Investment measures are the deciles rank of

investment measured in the fiscal year ending in calendar year t – 1 ranging from 0 to 9. HRDS is a dummy variable

that equals 1 if a firm’s R&D expenditure scaled by sales in year t – 1 is non-missing. Panels A and B report the

interaction with size and development costs, respectively. Big is a dummy that equals 1 if a firm’s size at the end of

June of year t is above the NYSE median size breakpoint. HDC is a dummy that equals 1 if a firm operates in the

following industries based on Fama-French 48 industry classifications: 12 (medical equipment), and 13

(pharmaceutical products), 27 (precious metals), 28 (mining), 30 (oil and natural gas), 32 (telecommunications). All

independent variables (except rank variables and dummies) are winsorized at the top and bottom 1%. Financial firms

and firms with assets below $25 million are excluded. The sample period for stock returns is from July of 1977 to

December 2011.

Panel A. Interaction with size

Panel A1. Investment = IG

Year IG IG*HRDS*Big HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.04 0.02 0.25 -0.09 0.24 0.57 1.70

(-4.54) (1.25) (2.67) (-1.99) (3.14) (2.58) (4.39)

2 -0.01 0.04 0.21 -0.13 0.12 0.49 1.78

(-0.74) (2.15) (2.15) (-2.75) (1.69) (2.20) (4.48)

3 -0.01 0.04 0.13 -0.15 0.03 0.45 1.86

(-0.64) (2.54) (1.28) (-3.02) (0.42) (2.02) (4.76)

4 -0.02 0.05 0.14 -0.16 -0.01 0.31 1.94

(-2.05) (3.17) (1.40) (-3.26) (-0.16) (1.34) (4.99)

5 -0.01 0.06 0.14 -0.15 0.01 0.27 1.83

(-1.05) (3.84) (1.43) (-3.09) (0.20) (1.14) (4.64)

Panel A2. Investment = IK

Year IK IK*HRDS*Big HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.03 0.02 0.27 -0.10 0.23 0.59 1.66

(-1.70) (1.56) (3.08) (-2.13) (3.40) (2.70) (4.61)

2 0.00 0.04 0.21 -0.13 0.13 0.50 1.75

(0.09) (2.43) (2.26) (-2.81) (2.01) (2.24) (4.77)

3 -0.01 0.05 0.12 -0.15 0.02 0.46 1.89

(-0.55) (2.98) (1.39) (-3.15) (0.27) (2.05) (5.13)

4 -0.01 0.05 0.14 -0.16 0.00 0.31 1.89

(-0.39) (3.41) (1.60) (-3.27) (-0.03) (1.32) (5.12)

5 0.00 0.06 0.14 -0.15 0.03 0.28 1.79

(-0.01) (3.65) (1.53) (-3.07) (0.48) (1.16) (4.81)

66

Panel B. Interaction with development costs

Panel B1. Investment = IG

Year IG IG*HRDS*HDC HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.04 0.06 0.24 -0.09 0.25 0.57 1.67

(-4.97) (2.48) (2.63) (-1.82) (3.30) (2.57) (4.26)

2 -0.01 0.05 0.22 -0.12 0.13 0.48 1.69

(-0.82) (2.09) (2.36) (-2.42) (1.86) (2.13) (4.28)

3 0.00 0.05 0.16 -0.13 0.04 0.44 1.76

(-0.54) (1.94) (1.69) (-2.73) (0.54) (1.96) (4.58)

4 -0.02 0.03 0.18 -0.14 -0.02 0.30 1.84

(-1.85) (1.21) (1.94) (-2.96) (-0.22) (1.31) (4.78)

5 -0.01 0.05 0.20 -0.12 0.01 0.27 1.67

(-0.58) (1.68) (2.11) (-2.66) (0.21) (1.12) (4.31)

Panel B2. Investment = IK

Year IK IK*HRDS*HDC HRDS ln(Size) ln(BTM) Momentum Intercept

1 -0.03 0.05 0.27 -0.09 0.24 0.59 1.60

(-1.74) (1.96) (3.10) (-1.91) (3.57) (2.70) (4.41)

2 0.00 0.05 0.22 -0.11 0.14 0.48 1.65

(0.09) (2.14) (2.45) (-2.44) (2.23) (2.17) (4.51)

3 -0.01 0.05 0.16 -0.13 0.02 0.44 1.75

(-0.37) (1.78) (1.83) (-2.78) (0.42) (1.97) (4.87)

4 0.00 0.03 0.19 -0.14 -0.01 0.30 1.76

(-0.15) (0.96) (2.18) (-2.95) (-0.14) (1.29) (4.85)

5 0.00 0.05 0.19 -0.12 0.03 0.27 1.63

(0.24) (1.61) (2.15) (-2.64) (0.47) (1.13) (4.46)