CEO compensation, diversification, and incentives

Journal of Financial Economics 66 (2002) 29–63

CEO compensation, diversification, andincentives$

Li Jin*

Harvard Business School, Boston, MA 02163, USA

Received 24 October 2000; accepted 13 November 2001

Abstract

This paper examines the relation between chief executive officers’ (CEOs’) incentive levels and

their firms’ risk characteristics. I show theoretically that, when CEOs cannot trade the market

portfolio, optimal incentive level decreases with firm’s nonsystematic risk but is ambiguously

affected by firm’s systematic risk; when CEOs can trade the market portfolio, optimal incentive

level decreases with nonsystematic risk but is unaffected by systematic risk. Empirically

I find support for these predictions. Furthermore, I find that incentives for CEOs likely

facing binding short-selling constraints decrease with systematic as well as nonsystematic risk,

as predicted by theory. Thus, compensation practice is consistent with predictions of theory.

r 2002 Elsevier Science B.V. All rights reserved.

JEL classification: J33; G30; G32; G34; G11

Keywords: Executive compensation; Diversification; Firm-specific risk; Incentives; Pay–performance

sensitivities

$I am indebted to my advisors, Andrew Lo, Robert Merton, Lisa Meulbroek, Stewart Myers, and

David Scharfstein, for numerous stimulating discussions, for encouraging me to pursue this topic, and for

advice on the paper. I am grateful to the extensive advice that I received from the referee, Kevin Murphy,

which substantially improved the paper. I thank Rajesh Aggarwal, Marianne Bertrand, Robert Gibbons,

Brian Hall, Bengt Holmstrom, S.P. Kothari, Jonathan Lewellen, Sendhil Mullainathan, Sarah Peck,

Andre Perold, Canice Prendergast, Jeremy Stein, Marti Subrahmanyam, Peter Tufano, Zhengyu Wang,

and seminar participants at Boston College, Boston University, Columbia University, Harvard University,

Lehman Brothers, Massachusetts Institute of Technology, Yale University, University of British

Columbia, University of Illinois, University of North Carolina, University of Southern California, and

the 2001 WFA meetings for their insightful comments and helpful discussions, and Robert Merton for

providing access to certain data used in this paper. Any errors are my own.

*Tel.: +1-617-496-5590; fax: +1-617-496-7197.

E-mail address: [email protected] (L. Jin).

0304-405X/02/$ - see front matterr 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 4 0 5 X ( 0 2 ) 0 0 1 5 0 - 2

1. Introduction

This paper examines the impact of imperfect diversification on chief executiveofficer (CEO) incentive level. CEOs’ direct pay is linked to the stock marketperformance of firms, and CEOs typically hold large equity stakes in their firms. Thedegree to which CEO wealth is linked to stock market performance is a measure ofincentive level.An extensive literature on executive compensation follows the early works of

Jensen and Meckling (1976) and Holmstrom (1979).1 It has been well demonstratedthat a trade-off should be made between providing incentives and optimal risk-sharing for CEOs and shareholders, such that incentive level should decrease withfirm risk. Most of the existing literature, however, assumes a risk-neutral principal. Asimple argument might be that a principal with sufficient wealth can eliminate risk.But in the financial market, even at the aggregate market level, risk does not cancelout. A truly risk-neutral representative investor in the financial market should bewilling to demand the same expected return from risky and riskless investments. Inreality, there is a positive and large market risk premium, which has averaged about7% per annum in the United States in the post-war period. The fact that this marketrisk premium is not arbitraged away suggests that the representative investor is stillsubstantially averse to systematic risk. This implies that it is costly for outsideshareholders, as well as for CEOs, to bear the market risk.Many existing theoretical works implicitly assume that CEOs cannot trade, that

either they hold all of their wealth (both capitalized future labor income andfinancial assets) in their firms or, even if they have a portfolio outside their firms,they cannot adjust it in response to their compensation contracts. Recent evidencesuggests that managers do adjust their outside portfolio holdings according to therisk characteristics of their firm-specific assets so as to hedge some of the risk theyaccrue from their firms.2 Whereas the hedging of firm-specific price movement actsagainst the intention of increasing incentives and is sometimes illegal, incentives arenot damaged if managers adjust their exposure to market risk through trading of themarket portfolio. It would thus be valuable to study how CEOs’ ability to trade themarket affects incentive level. I find that the incentive contract is different whenCEOs can trade the market portfolio.

1Representative pioneering works in CEO compensation include Coughlan and Schmidt (1985),

Demsetz and Lehn (1985), Murphy (1985, 1986), Lambert and Larcker (1987), Jensen and Murphy (1990),

Gibbons and Murphy (1992), and Smith and Watts (1992). Some recent papers on CEO compensation

include papers by Aggarwal and Samwick (1999), Bertrand and Mullainathan (2000), Carpenter (1998),

Core and Guay (1999), Garen (1994), Hall and Liebman (1998), Himmelberg et al. (1999), Holmstrom

(1999), Meulbroek (2000, 2001), Prendergast (2002), and Yermack (1995). Murphy (1999) conducts an

excellent survey on executive compensation.2For example, ‘‘Executive Relief,’’ Economist, April 3, 1999, p. 64, reports that the use of derivatives to

hedge managerial exposure to firm risk has become a business of hundreds of millions of dollars. Also,

Louis Lavelle, in ‘‘Undermining Pay for Performance,’’ Business Week, January 15, 2001, p. 70, reports

some recent incidences of executives hedging using zero-cost collars. Bettis et al. (2001) study executives’

increasing use of zero-cost collars.

L. Jin / Journal of Financial Economics 66 (2002) 29–6330

Empirically, Aggarwal and Samwick (1999), Garen (1994), and Kraft andNiederprum (1999) show that executive pay in riskier firms responds less to the firms’stock market performance than does executive pay in less risky firms, confirming theprediction of principal–agent theory. Existing empirical work, however, focuses ontotal risk instead of its components in testing the relation between risk and incentivelevel. Intuitively, it might be expected that market risk and firm-specific risk matterdifferently to incentives. First, although it is costly for both outside shareholders andCEOs to bear market risk, diversified shareholders have a clear cost advantage inbearing firm-specific risk because CEOs typically hold large positions in their firmsand are thus undiversified. Second, although CEOs might be able to trade the marketportfolio to adjust their exposure to systematic risk, for incentive reasons they arerequired to maintain nonsystematic (firm-specific) risk.I start by explicitly modeling the different effects of systematic and nonsystematic

risk on incentive levels. I assume both shareholders and CEOs to be risk-averse.Because incentive-based compensation leaves them with large stakes in their firms,CEOs are unable to fully diversify their exposure to firm-specific risk. Shareholders,meanwhile, are assumed to hold diversified portfolios and value stock according toits market valuation. It is clearly more costly for CEOs than for shareholders to bearfirm-specific risk, but it is unclear whether it is also more costly for CEOs to bearmarket risk. I demonstrate that the optimal incentive level decreases with firm-specific risk, but it can either increase or decrease with market risk. I also modelcases in which CEOs can adjust their exposure to market risk through trading of themarket portfolio but must retain firm-specific risk for incentive reasons. I find thatthe optimal incentive level decreases with firm-specific risk but does not change withmarket risk. Theory shows that the main cost of CEO incentives is loss ofdiversification by forced exposure to substantial firm-specific risk.I empirically investigate whether decomposing risk into its systematic and

nonsystematic components might better explain the observed relation betweenincentives and risk. I find nonsystematic, but not systematic, risk to account fordocumented negative relation between risk and incentives. Controlling for the levelof systematic risk, I find nonsystematic risk level to be negatively related to incentivelevel, but controlling for the level of nonsystematic risk, I find no significant relationbetween systematic risk and incentive level. This finding is robust to a variety ofregression methods, different ways to decompose risk into systematic andnonsystematic risk, and adding control variables known to influence incentive levels.Although in theory CEOs could fully adjust their market risk exposure through

trading, in reality constraints might be placed on doing so. An incentivecompensation contract that incurs greater market risk than can be fully hedgedthrough trading might leave a CEO with more than optimal market risk. As it mightbe more costly for such CEOs than for shareholders to bear market risk, the optimalincentive level should decrease with a firm’s market as well as firm-specific risk.Empirically, I test for a negative relation between incentives and market risk levelsfor a subsample of CEOs who have above-average equity holdings in their firms (andthus are more likely to be constrained from optimizing their market risk exposure).I find some support for this negative relation.

L. Jin / Journal of Financial Economics 66 (2002) 29–63 31

This paper is organized as follows. Section 2 presents theoretical models thatillustrate the optimal trade-off between incentives and loss of diversification. Section3 describes the data set. Section 4, which empirically tests the optimal trade-offbetween diversification and incentives in CEO compensation, demonstrates thatfirm-specific risk is significantly negatively related, and systematic risk ambiguouslyrelated, to incentive level. Section 5 discusses the robustness of the empirical findings.Section 6 offers concluding remarks. Proofs and some technical details are presentedin Appendix A.

2. The models

A principal-agent model is employed to analyze the trade-off between grantingCEOs high incentives and letting them bear (inefficiently) firm-specific risk. Granted,the trade-off between incentives and insurances is not the only explanation for thepattern of CEOs’ large stake in their own firms.3 No matter what the ultimate reasonfor CEOs to hold undiversified positions in a single firm, it is useful to study the costof doing so, which can always be measured by the level of underdiversification.4 Forthe theory models presented below, I assume CEOs to hold undiversified positions tomaintain incentives. Certainly this can be generalized.I assume CEOs to be risk-averse and to hold disproportionally large amounts of

stock and options in their firms and, consequently, to care about both systematic andnonsystematic risk. I assume outside shareholders to be well-diversified investorswho value the firm as the market does. Finally, I assume firm-specific risk to beexogenous and thus beyond the control of the CEO.5

Following the classical papers of Holmstrom and Milgrom (1987, 1991), I assumethe compensation contract to take a linear form that rewards CEOs for both marketand firm-specific performance.6 But I show that the sensitivity of CEO pay to firmperformance is affected differently by firm-specific and systematic risk. In particular,although higher firm-specific risk makes the ex-ante compensation contract less

3See Gibbons (1998) for some new trends in agency theory trying to explain incentives in real

organizations and Dammon et al. (2000) for tax-related reasons for CEOs’ equity holdings in their firms.4Meulbroek (2001) performs just such calculations and finds that managers at the average NYSE firm

who have their entire wealth invested in the firm value their options at 70% of their market value, while

undiversified managers at rapidly growing, entrepreneurially based firms, such as Internet-based firms, on

average value their option-based compensation at only 53% of its cost to the firm.5Theoretically, CEOs can affect their firms’ risk levels in response to existing incentive schemes. Recent

empirical studies such as that of Aggarwal and Samwick (2001) show that CEOs do not seem to optimize

their firms’ risk characteristics in response to incentive schemes. Still, as a robustness check, I discuss in the

empirical section instrumental variable approaches that address the endogeneity of risk.6The optimality of the linear sharing rule depends critically on the assumption of a constant absolute

risk aversion utility function, of which the mean–variance optimization can be construed as a reduced

form. With more general preference, a linear contract might not be the optimal contract. In practice,

however, the sharing rule is often close to linear because the convexity induced by CEO options holdings is

negligible to the first order; for a return change one standard deviation above or below the median return

level, the slope of an incentive contract typically changes about 1–2%.


performance-dependent, higher systematic risk might not. I study two models. Inboth, the outside shareholder is modeled as a representative investor who values thecompany using the Capital Asset Pricing Model (CAPM).7 In the first model Iassume that the CEO cannot trade on the financial market and thus must hold therisk that attends the compensation package. In the second model I assume that theCEO can trade without restriction a market portfolio but, to maintain incentives,cannot hedge—either explicitly or implicitly—firm-specific risk.8

2.1. Model I: CEO cannot trade the market portfolio

In this subsection, the CEO is assumed to be able to take neither a long nor a shortposition in the out-of-firm portfolio. For example, the CEO has no out-of-firmwealth to invest. The only source of risk is thus the CEO’s compensation package.Shareholders, because they can trade freely on the financial market and optimallychoose to hold a diversified portfolio, value their payoff from the firm by CAPM.The firm’s initial market capitalization is x: Its next period market capitalization is

*X ¼ xð1þ grfirmrfirmÞ; where grfirmrfirm is the firm’s net percentage return over the next period.Using CAPM, I arrive at grfirmrfirm ¼ rf þ bðfrmrm � rf Þ þ *e; where b is the firm’s beta, rf is

the risk-free interest rate, andfrmrm and *e are the market return and firm-specific return,respectively. This can be reorganized to *X ¼ x½1þ rf þ bðrm � rf Þ þ xbðfrmrm � rmÞ þx*e� where rm is the expected market return.The firm’s next period market capitalization can be decomposed into the mean

component and two zero-mean components that correspond to the systematic andfirm-specific risk, respectively. To simplify notations, the foregoing expression isreplaced in the following analysis by

*X ¼ %X þ Zðfrmrm � rmÞ þ *d; ð1Þ

where Z ¼ xb is the firm’s market capitalization times its beta, a measure of the firm’smarket risk; and *d ¼ x*e represents the firm’s dollar firm-specific risk. I defineVarðfrmrm � rmÞ ¼ s2m as the variance of the market portfolio’s percentage return andVarð*dÞ ¼ s2d as the variance of the dollar firm-specific risk.I assume that the expected next period firm value, %X; can be affected by CEO

effort level e in a linear way: %X ¼ X0 þ ke; whereX0 is the mean firm value when the

7I assume CAPM for simplicity of exposition. No insight would be lost by using any other asset pricing

model, and the same result would be obtained by modeling the principal as a risk-averse investor who can

trade on the financial market to optimize exposure to market risk. The proof can be obtained from the

author.8The last assumption, although seemingly natural, can be violated in practice. Ofek and Yermack (2000)

show that following the reward of new, equity-based compensations executives sometimes sell off some of

their firms’ stocks to diversify. Schizer (2000) discusses the practice of short-selling a tracking portfolio of

highly correlated stocks. In recent years, investment banks have aggressively engaged in internal risk

management for executives by structuring the zero-cost collar, which reduces their firm-specific risk (and

thus incentives). There is no evidence that homemade risk management by executives would have a

substantial and systematic effect. For simplicity I assume away such complications, although I point out

that increased risk management over time might help to explain the apparent increase in CEO incentive

levels over time.


CEO exerts zero effort and k is the productivity of CEO effort, which is assumed tobe a constant. I assume that exerting effort incurs on the part of the CEO (agent) anunobservable cost that can be expressed in monetary terms as f ðeÞ: f ðeÞ is increasingand convex, so that as the effort level increases, the total cost increases more thanlinearly.9 To simplify the solution, I assume f 00ðeÞ to be a constant.10

The principal gives a linear contract to the agent: pA ¼ b *X þ s; where pA is thecontract’s payoff to the agent and b and s are constants. The principal’s payoff isthus pP ¼ ð1� bÞ *X � s: I assume that the agent has mean variance optimizationpreferences, thus

UAðwÞ ¼ EðwÞ �1

2gAVarðwÞ; 8w: ð2Þ

The certainty equivalent total payoff of the agent, including cost of effort, is

CEA ¼ b %X þ s � f ðeÞ� �

�1

2b2gAðZ

2s2m þ s2dÞ: ð3Þ

Using CAPM, it can be proved that the certainty equivalent payoff of the principal is

CEP ¼ ð1� bÞ½ %X � Zðrm � rf Þ� � s: ð4Þ

The principal’s problem can thus be written

maxb;s;eð1� bÞ½ %X � Zðrm � rf Þ� � s; ð5Þ

st:½b %X þ s � f ðeÞ� �1

2b2gA Z2s2m þ s2d

� �XCEA; ð6Þ

and

½b %XðeÞ þ s � f ðeÞ� �1

2b2gAðZ

2s2m þ s2dÞX½b %Xðe0Þ þ s � f ðe0Þ�

�1

2b2gAðZ

2s2m þ s2dÞ;8e0; ð7Þ

where Eq. (6) is the individual rationality constraint with CEA being the reservationlevel of payoff, and Eq. (7) the incentive compatibility constraint for e to be theoptimal choice of effort level.When f ðeÞ is first-order differentiable, Eq. (7) can be replaced by the first-order

condition f 0ðeÞ ¼ bk:

9The assumption of linear impact and convex cost of effort can be thought of as a reduced form of the

more general assumption that the cost of effort is convex and increasing (increasing marginal cost of

effort) and the effect of effort is concave and increasing (diminishing marginal benefit of effort) because

the effort unit can always be rescaled to make it linear in output and the resulting cost function of effort

will be convex. A simple proof can be obtained from the author. In a more general setting, in which, for

example, the impact of CEO effort has an increasing but nonconvex functional form, the optimization

problem of principal might not have a unique interior solution.10 In both models discussed in this paper, the results can be generalized to allow for a more general cost

of effort function. Interested readers could obtain details and proof from the author.


The above problem has the solution

b ¼Zðr!m � rf Þ þ k2=f 00ðeÞ

gAðZ2s2m þ s2dÞ þ k2=f 00ðeÞ; ð8Þ

e ¼ f 0ð�1Þðb kÞ; ð9Þ

and

s ¼ CEA � ½b %X � f ðeÞ� þ1

2b 2 gAðZ

2s2m þ s2dÞ: ð10Þ

The proof is provided in Appendix A.This result has three important implications.

1. Pay–performance sensitivity (PPS) b decreases in firm-specific risk, s2d; becausehigher firm-specific risk increases the cost of lost diversification of the CEO, andthus the cost of providing incentives.

2. The relation between market risk level (Z) and pay–performance sensitivity (b) isambiguous. When Z is high, b could be either high or low depending on the otherparameters. Intuitively, the marginal cost of bearing market risk for the principalis determined by the market price of (market) risk, reflected by rm � rf ; but theagent’s marginal cost of bearing market risk is determined by his or her risk-aversion coefficient gA and his or her exposure to market risk in the compensationcontract, Z2s2m: The agent might have a lower marginal cost of bearing market riskbut might not be able to load up such risk by trading outside the firm for reasonssuch as a liquidity constraint. Consequently, when a firm’s market risk levelincreases it will be optimal to increase the incentive, b :

3. A positive relation exists between the productivity of CEO effort, k; and pay–performance sensitivity, b : Higher productivity of CEO effort makes the effortmore valuable to the firm, thus increasing the shadow price of the incentivecompatibility constraint. The incentive level therefore increases.

2.2. Model II: CEO can trade the market portfolio

I now consider the case in which the CEO can trade the market portfolio andthereby fully adjust exposure to the market risk. Specifically, an arbitrarily positiveor negative amount can be invested in the market portfolio and the balance of CEO’swealth put in a long or short position in the risk-free asset.Denote by IA the CEO’s (agent’s) dollar investment in the market portfolio. The

firm’s total payoff to the agent, after accounting for the agent’s investment in themarket portfolio (financed by a corresponding reduction in the agent’s position inthe riskless asset) and cost of effort, becomes

p0A ¼ b *X þ s � f ðeÞ þ IAðfrmrm � rf Þ ¼ b %X þ bZþ IAð Þðfrmrm � rmÞ

þ b*dþ IAðrm � rf Þ þ s � f ðeÞ: ð11Þ


The agent’s certainty equivalent payoff can be written as

CEA ¼ b %X þ s � f ðeÞ �1

2gA bZþ IAð Þ2s2m þ b2s2d

� �þ IA rm � rfð Þ: ð12Þ

I first derive the agent’s optimal level of investment in the market. Given thecompensation contract, the agent is trying to set IA and e to maximize the certaintyequivalent payoff. Note that the agent’s optimization over IA can be separated fromthat over e: Following the convention in the principal–agent literature, the agent’soptimization problem over e will be addressed within the principal’s problem as theincentive compatibility constraintThe first-order condition in the above problem with respect to IA is

ðrm � rf Þ � gAðbZþ IAÞs2m: ð13Þ

Solving it yields the agent’s optimal level of investment in the market

IA ¼rm � rf

gAs2m� bZ: ð14Þ

To help developing intuition, we first analyze two benchmark cases. First, whenthe market risk premium, rm � rf ; is zero, IA ¼ �bZ: That is, in the absence of anequity risk premium it is always optimal for an executive to completely back out themarket risk embedded in a compensation contract by appropriately shorting themarket portfolio. Second, if the firm has no systematic risk (zero beta stock), inwhich case Z ¼ 0; or, alternatively, if the agent’s compensation contract has a slopeof zero (b ¼ 0), then IA ¼ ðrm � rf Þ=gAs

2m: This is the optimal market risk exposure

that any outside investor with identical risk aversion would have chosen: to invest inthe market portfolio until the marginal benefit of a higher expected return is equal tothe marginal cost of a higher volatility of the portfolio. Taken together, given apositive market risk premium, the agent’s optimal behavior is to (1) completely backout exposure to the market risk embedded in the compensation contract and (2)subsequently reload exposure to the market risk to a level that is optimal to anyoutsider with the same risk aversion. The sign of IA will depend on the agent’s riskaversion as well as the level of market risk embedded in the compensation contract.The principal’s problem can thus be written as

maxb;s;eð1� bÞ½ %X � Zðrm � rf Þ� � s; ð15Þ

st: b½ %X � Zðrm � rf Þ� þ s � f ðeÞ þ1

2

ðrm � rf Þ2

gAs2m�1

2gAb2s2dXCEA; ð16Þ

and

gðeÞXgðe0Þ;8e0; ð17Þ

where

gðeÞ ¼ b½ %XðeÞ � Zðrm � rf Þ� þ s � f ðeÞ þ1

2

ðrm � rf Þ2

gAs2m�1

2gAb2s2d: ð18Þ


When f ðeÞ is first-order differentiable, Eq. (17) can be replaced by the first-ordercondition, f 0ðeÞ ¼ bk:The problem has the solution

b ¼k2

gAs2d f 00ðeÞ þ k2; ð19Þ

e ¼ f 0ð�1Þðb kÞ; ð20Þ

and

s ¼ CEA � b %X � f ðeÞ � bZðrm � rf Þ þ1

2

ðrm � rf Þ2

gAs2m�1

2gAb 2 s2d

� �: ð21Þ

The proof is provided in Appendix A.The result has three important implications.

1. Pay–performance sensitivity b decreases in firm-specific risk s2d as before.2. Firm exposure to market risk, Z; does not affect b: Because both principal andagent can trade the market portfolio, they equalize their marginal cost of bearingthe market risk and make it equal to the market price of market risk. Thus, initialdivision of market risk through the incentive plan does not matter because anyparty can adjust suboptimal exposure to the market risk by trading the marketportfolio.

3. The higher the productivity of effort (k), the higher pay–performance sensitivity.

The result in equation Eq. (19) resembles that of standard pay–performancesensitivity in a model in which the principal is risk-neutral and the volatility ofperformance is s2d: This result will hold even when the principal is risk-averse andvalues the stock as the financial market does, although the appropriate risk measurewill then be firm-specific, not total risk. That is to say, when the two parties canindependently invest in the market the optimal contract will be purely an incentivecontract involving the trade-off between incentives and the agent’s forced loss ofdiversification. In contrast, Eq. (8) reflects both an incentive contract and optimalrisk-sharing between the two parties. The incentive contract component can beisolated by considering the case of Z ¼ 0; the optimal risk sharing component, byconsidering the case of k ¼ 0:

2.3. Extensions

The above models can be extended to more general cases, and in what follows Idiscuss three extensions. In the first extension, the CEO can long, but not short, themarket. In the second extension, CEO cannot trade the market portfolio at all, butfirm can contract separately on the systematic and firm-specific performance of thefirm. The third extension deals with the case where firm can use another signal tosupplement the stock market performance in designing the compensation contract.


2.3.1. CEO cannot short the market

The optimal out-of-firm investment in the market portfolio, IA; for an agent whocan freely trade the market portfolio, can be either positive or negative depending onthe agent’s risk aversion and the level of market risk embedded in the compensationcontract. In particular, as demonstrated in Eq. (14), when bZ is large, other thingsbeing equal, the optimal investment in market portfolio IA will tend to be negative.Theoretically, CEOs could completely adjust their market risk exposure by trading

the market portfolio, but realistically there are constraints to doing so. Although inpractice CEOs could buy or sell a large futures contract on the Standard & Poor’s(S&P) 500 without investing the full amount, a margin payment would be requiredex ante. In addition, concerns about unlimited liabilities in shorting the S&P futurescontract might limit the extent to which CEOs want to engage in such trading.Consequently, incentive contracts that attend more market risk than can be hedgedwill leave the CEOs with more than optimal market risk. In that case, it can beproven that it is more costly for CEOs than for shareholders to bear market risk, andthe optimal incentive level unambiguously decrease with firm’s market risk level. Forthe sake of brevity, the proof is omitted (interested readers can obtain it from theauthor).Therefore, a second cost of incentive contracts is the CEOs’ nonoptimal exposure

to market risk. Even here, however, CEOs are rewarded for holding market riskinstead of the riskless asset by a substantial market risk premium. In other words,there is in this case a cost advantage to the diversified shareholder over the CEO tobear more firm-specific risk and a lesser cost advantage to the shareholder over theCEO to bear more market risk. The nonoptimality of CEOs’ market risk exposure isa secondary cost compared with the cost of lost diversification, and thenonsystematic and systematic risk will have different impacts on incentive level.In the empirical analysis, I identify cases in which the CEOs are less likely to be

able to freely adjust their market risk exposure and find the prediction in the abovediscussion is more relevant there.

2.3.2. CEO cannot trade, but firm contracts separately on systematic and firm-specific

performance

Assuming that CEOs can trade the market portfolio is not the only way to arriveat the findings in Section 2.2 that market risk is irrelevant to incentive level.Functionally equivalent results are obtained when CEOs cannot trade the market,but firms can contract separately on firm-specific and market performance. Theproof can be obtained from the author. This result is closely related to the notion ofrelative performance evaluation, which argues that CEOs should be rewarded forfirm performance net of any performance caused by general movement of themarket. In practice, relative performance evaluation is not frequently observed. Thetheory model demonstrates that relative performance evaluation can be welfare-increasing if CEOs are severely constrained from hedging market risk exposure. Thisresult is consistent with the findings of Garvey and Milbourn (2001) incontemporaneous work, which finds significant evidence of relative performance


evaluation for executives who face relatively high cost of removing excessive marketexposure on their own account.

2.3.3. Contracting on another signal

In light of the argument by Holmstrom (1979), not only firm output, but othersignals of CEO effort such as accounting measures of performance, could beoptimally included in the compensation contract. Prendergast (2002) posits thatdirect monitoring of CEO effort is more difficult when risk increases. Accountingnumbers, for example, become less meaningful. In this case, firms might rely moreheavily on incentive plans to align CEO incentives, thus there will be a substitutionbetween monitoring and effort.Theoretical models can be constructed to incorporate these extensions and

empirical tests modified to address the attendant concerns. For brevity, theseextensions are not included. Interested readers can find a detailed discussion in Jin(2001).

3. Data and measurement of variables

My primary data set for executive compensation is the ExecuComp databasemaintained by Standard & Poor’s. This data set reports annual compensation for thefive most highly paid executives, including the CEO, for each firm in the S&P 500,S&P mid-cap 400, and the S&P small cap 600 from 1992 to 1998. Levels of salariesand bonuses and the value of other types of grants in each year, as well as the CEOs’holdings of their firms’ stocks and stock options, are reported. I construct from thisdata set, which represents 2,018 unique firms and 9,714 CEO-year observations, ameasure of CEO incentives.Stock price information obtained from the Center for Research in Security Prices

daily and monthly stock files and the accounting variables obtained fromCOMPUSTAT are used to construct the risk measures and control variables.

3.1. Measuring incentives

As discussed in the literature, firm performance influences both CEO capitalizedfuture labor income and financial wealth. The standard measure of CEO incentives ispay–performance sensitivity, defined by Jensen and Murphy (1990) as the totalchange in CEO wealth resulting from a $1,000 increase in shareholder value. PPSfrom CEOs’ financial wealth is captured by the reevaluation of their holdings ofstock and stock options in their firms as a result of firm performance. PPS fromCEOs’ capitalized future labor income change is captured by the present value of thechange in all the future labor income cash flow as a result of their firms’performance. A detailed discussion of the construction of the PPS measure isprovided in Appendix A.Hall and Liebman (1998), among others, show that changes in CEOs’ financial

capital accounts for nearly all of pay–performance sensitivity. It can be measured


relatively precisely compared with the imprecise regression approach required toestimate PPS from capitalized future labor income changes. Consequently, theempirical results presented here focus mainly on PPS from CEOs’ financial wealth.Results using the total PPS, included as a robustness check, are essentially thesame.11

Jensen and Murphy’s (1990) measure of the pay–performance sensitivity measuresthe effective percentage ownership of CEOs in firms, where CEOs’ holdings of stockoptions and performance-based labor income are converted into effective holdings inthe firm’s stock. This measure is, as pointed out by many researchers, consistent withstandard agency models in which performance and risk are measured in dollars. Toaddress the empirical regularity that dollar pay–performance sensitivity decreaseswith firm size, I explicitly control for firm size by adding the standard control oflog(sales) and square of log(sales) in the regression analysis below.12

3.2. Measuring risk

To be consistent with standard agency theory, risk is also measured in dollars,which renders it roughly invariant to changes in firm leverage. If debt is assumed tobe riskless, total dollar risk of firm equity will remain constant even as the percentagerisk of firm equity changes with firm leverage. I obtain dollar risk measures bymeasuring the variance of percentage returns and multiplying by the square of thebeginning-of-period firm value.The percentage systematic and firm-specific risk is measured several different

ways. The traditional way to decompose total risk into systematic and firm-specificrisk is through a market model regression, firm-specific risk being the mean-squarederror and systematic risk the beta-squared multiplied by the variance of marketreturn. My basic risk measure is derived from the market model regression using upto 60 monthly observations immediately before the current calendar year. As arobustness check, I also perform empirical tests using risk measures constructedfrom market model regression of up to one year or up to three years of weekly data,adjusted for the potential of nonsynchronous trading by adding lagged returns. Theresults, omitted for brevity, are similar to those reported here. A Fama-French three-factor model and regression free approach are also used to decompose risk. Theseare discussed in greater detail in Section 5.Two considerations motivate the use of industry average percentage risk measures

to replace individual firm risk measures before constructing dollar risk measures.First, measurement errors introduced by the market model regression are not likely

11 In practice, managers with better performance histories might be able to move up to better, higher

paying jobs. It might be the case that although the observed capitalized future labor income within the firm

does not move much with performance, the outside market value of the manager increases considerably

because of good performance. If so, the pay–performance sensitivity of capitalized future labor income

estimated in the traditional way might underestimate the true pay–performance sensitivity.12The dollar measure is not without controversy. Baker and Hall (1998), for example, show that

although the dollar measure will be appropriate if the CEO’s action has the same dollar impact on firm,

the percentage measure will be more sensible if the CEO’s action has the same percentage impact.


to be correlated with industry classification. The idea of forming portfolios to reducerisk measurement errors has been extensively explored in the empirical asset pricingliterature, following the papers by Fama and MacBeth (1973) and Fama and French(1992). Second, CEOs can potentially control the level of their firms’ risk, in whichcase, a more robust measure of the environmental risk level would be the industryaverage risk level, which CEOs are less likely to be able to manipulate. As arobustness check, I also calculate the risk decomposition of the value-weightedindustry portfolio directly and assign the percentage risk measures to firms withinthe same industry. Although this approach yields similar results, a potentialdrawback is that if large firm-specific risk is cancelled out when the industryportfolio is formed, then the nonsystematic risk on industry portfolio will not reflectthe real average firm-specific risk.Alternatively, individual firm risk measures might be treated as independent

variables and the industry average risk measures as instrumental variables. In thisway, more individual firm-level information could be used and the measurementerror problem still be addressed. The instrumental variable approach is more sensiblewhen there is a possibility of endogeneity of risk measures, given that CEOs mightchoose their firms’ risk levels in response to the incentive schemes they are offered.13

A version of the test using this instrumental variable approach, reported below,yields qualitatively similar results.The raw risk measures thus obtained are not of the same order of magnitude and

exhibit a large amount of variation. Taking 1995, for example, the raw risk measuresare extremely right-skewed and fat-tailed (skewness of 18 and extra kurtosis of morethan 400). There is also, although the majority of risk measures are concentrated in avery small region, a wide range of values of the raw risk measure. Median total risk isabout five times larger than the 25th percentile risk, the 75th percentile risk measurealmost 10 times larger than the median risk, the 90th percentile risk more than 1,000times larger than the 10th percentile risk, and the maximum raw risk measure 8.6million times larger than the minimum raw risk measure. The firm-specific andsystematic risk measures exhibit similar patterns.The problem is not easily addressed by removing the outliers. Truncating the data

at the 1% and 99% levels yields a data set that is almost as dispersed as the original,the 99th percentile data being five orders of magnitude larger than the 1st percentiledata.To make the regression results economically more sensible, I need to find a

transformation that can make the highly nonhomogeneous data more homogeneous.Following Aggarwal and Samwick (1999) and Bertrand and Mullainathan (2000),I construct the rank of risk measures among all firms in the ExecuComp database.I report regression results where rank measures of risk are used.The rank of risk measures, as pointed out by Aggarwal and Samwick (1999), give

the regression results more economic intuition. Using the rank of risk measures,I can easily transform the regression coefficients into pay–performance sensitivities

13For a detailed discussion of the use of the instrumental variable approach to deal with measurement

errors and endogeneity of variables, see, for example, Greene (1993).


at any percentile of the distribution of risk. Were I to use the highlynonhomogeneous raw risk measures, the results would be less interpretable.Rank of risk measure is not the only way to transform the risk measure to make it

more homogeneous. I also use a log transformation of the raw risk measures andreport the results in this paper.

3.3. Controlling for size and the benefit of giving incentives

I include control variables to address the size-related heterogeneity of PPS andpositive effect of CEO effort productivity on PPS.14

The cross-sectional level of CEO pay–performance sensitivity changes predictablywith firm size: Larger firm’s CEOs have lower pay–performance sensitivity. Toensure that my results are driven not just by size, I add log(sales) and the square oflog(sales) in the regression analysis as control variables.15

I could also measure firm size by the market capitalization. As Berk (1995) pointsout, however, market capitalization can be thought of as a catch-all for the missingfactors that price the stock. Thus, I might inadvertently use the size proxies to proxyfor the risk.A large literature on the benefit of giving incentives argues that the more valuable

the CEO’s effort is, the higher the incentive should be, holding everything elseequal.16 In particular, Prendergast (2002) argues that risk could be positively relatedto the value of CEO discretion, which, in turn, is positively related to incentive level.Thus, if the positive effect of risk on incentive (through more valuable managerialdiscretion) dominates the negative effect of risk on incentives (through lack ofmanagerial diversification), then a positive relation could be observed between riskand incentives. To better capture the cross-sectional variation in the benefit of givingCEOs incentives, direct control variables on the value of CEO effort have beenadded in my empirical tests. These variables include the ratio of capital over sales,

14These control variables are essentially the same as those used by Himmelberg et al. (1999) and

Aggarwal and Samwick (2001).15The relation between size and PPS is addressed in greater detail by Jensen and Murphy (1990), Baker

and Hall (1998), Schaefer (1998), and Garen (1994), among others. I do not analyze this relation beyond

the existing research. Previous research documented that risk and log of firm size are approximately

linearly related, thus adding log(size) seems a natural way to control for size effect. The addition of the

square of log(size) is aimed at controlling for the remaining nonlinear relation between log(size) and PPS.

The use of log(size) and the square of log(size), however, is meant to control only for the PPS–size relation.

It by no means suggests that the true relation between log(size) and PPS is quadratic. Although not

reported, I have run the tests by controlling for log(sales) alone, or by controlling for log(sales), square of

log(sales), and cube of log(sales) all together, and found the resulting risk–PPS relation to be qualitatively

the same.16Existing researches such as Smith and Watts (1992) and Hubbard and Palia (1995) find higher pay–

performance sensitivities for CEOs after deregulation, or when firms have larger investment opportunity

sets, consistent with the hypothesis that a higher incentive level is needed when CEOs’ effort becomes more

valuable. In a recent paper, Core and Guay (2002) documented that a positive relation between risk and

incentive could be obtained under certain regression specification, if the benefit of giving incentives

through other variables is not controlled. Jin (2001) provides a much more detailed analysis of the benefits

of giving incentives and comment on the Prendergast critique.


research and development (R&D) expense over capital, advertising expense overcapital, dummy variables for missing observations of the last three variables, and theratio of investment expense over capital. I also add the year dummies.

4. Testing the effects of risk on PPS

This section tests the predictions of the theory models. The results extend therecent work of Aggarwal and Samwick (1999), who find total risk to be negativelycorrelated with pay–performance sensitivity under various regression specifications.To deal with outliers, the existing literature on CEO compensation proposes the

use of median, robust, and ordinary least squares (OLS) regression.17 I perform allthree types, which generally yield qualitatively similar results. I also performregression controlling for firm or industry fixed effects and find that the results donot change qualitatively. The fixed effect regression results, omitted here for brevity,are provided in Jin (2001).18

In reporting the regression results, I report the coefficients, standard errors, andgoodness-of-fit measures.19

4.1. Point estimates

Aggarwal and Samwick (1999) show that a firm’s total risk is negatively related topay–performance sensitivity. I study whether firm-specific or market risk or bothcontribute to this effect.

17Median regression, used by Aggarwal and Samwick (1999), minimizes the sum of absolute deviations

instead of the sum of squared deviations so that the precise value of the dependent variable in a median

regression matters only in determining whether the observation has a positive or negative residual. If the

residual is positive or negative, the dependent variable can increase toward infinity (minus infinity) without

affecting the estimated parameters. Koenker and Bassett (1982) discuss the properties of median

regression. Hall and Liebman (1998) use robust regression to perform an initial screening based on

regression results and eliminate gross outliers, and they use the remaining observations and an iterative

method that minimizes a weighted sum of squared errors to perform regression. For details on robust

regression, see Street et al. (1988).18An intrinsic problem with the interpretation of fixed effect regression in this setting is that the

predictions of the model are cross-sectional by nature such that firms with higher firm-specific risk have

lower pay–performance sensitivity. If the firm-specific risk levels of firms do not change much over time,

including the fixed effect will result in attributing much of the risk-induced PPS change to the fixed effect.19Whenever the STATA program (the statistical package that I used) gives a sensible measure of

goodness-of-fit, I report that measure. Thus, I report adjusted R-squared for the OLS regression and later

for the instrumental variable regression as well as the pseudo R-squared for the median regression.

Because no sensible goodness-of-fit measure is directly reported for the robust regression in STATA, I

constructed a comparable measure by first running the robust regression to generate the weights the robust

regression assigns to each observation and then running a weighed OLS regression to obtain the adjusted

R-squared from that regression. Interested readers can contact the author for details of and the logic

behind this method.


I first run the regression

PPS ¼ aþ b1Total Risk þ b2Control Variables þ e ð22Þ

in which, as in Aggarwal and Samwick (1999), I regress the PPS measure on totalrisk, except that I add control variables discussed above. I perform OLS, median,and robust regressions. The results are reported in Table 1. For example, thecoefficient on the rank of total risk variable in the OLS regression of �0.505 isnegative and significant, suggesting a negative relationship between PPS and totalrisk. All the results support the basic findings of Aggarwal and Samwick (1999), thatan apparent negative relation exists between PPS and total risk measure, controllingfor many other variables.To determine whether the negative relation between risk and incentives is driven

by total risk or, specifically, firm-specific risk, I add the measure of firm-specific riskto the first regression. The new regression becomes

PPS ¼ aþ b11Total Risk þ b12Firm Specific Risk

þ b2Control Variables þ e: ð23Þ

Table 2 reports the regression results for OLS, median, and robust regressions.Although the coefficients on firm-specific risk measures are all negative andsignificant when total risk is included, the coefficients on total risk measure generallybecome insignificant when firm-specific risk measures are included. For example, inthe robust regression, the coefficient on rank of firm-specific risk is �0.109 andsignificant, while the coefficient on rank of total risk is �0.010 and insignificant.As a direct test of the hypothesis in Section 2, it is important to know what

happens when the total risk is decomposed into its systematic and firm-specific riskcomponents, and both are included in the regression. These adjustments yield theregression

PPS ¼ aþ b11Systematic Risk þ b12Firm Specific Risk


Table 3 reports results for OLS, median, robust, and instrumental variableregressions. In the instrumental variable regression, to address the measurementerrors in individual firm risk measures and account for the endogeneity of risk, I usethe individual firm’s rank of risk measures as independent variables and the industryaverage rank risk measures as instruments. The coefficients on firm-specific riskmeasures remain significant both economically and statistically across variousspecifications. The coefficients on systematic risk measures are generally insignif-icant.PPS from CEO financial wealth is an incomplete measure of total CEO incentives.

A less precise, but more comprehensive, measure of total CEO incentives is PPS fromboth financial wealth and capitalized future labor income changes. As a robustnesscheck I repeat in Table 4 the exercise in Table 3 but add to the PPS from CEOfinancial wealth the PPS from the change in capitalized future labor income. Theresults are essentially the same.


Rank measure is not the only way to transform the data to make it morehomogeneous. Another natural way to do this, often explored in other contexts, isvia a log transformation of the raw risk measures. I repeat the analysis using thatmeasure. Table 5 reports the results when I repeat the regressions in Table 3 usingthe log instead of the rank of risk measures. Again, the results are much the same,save that in the two OLS regressions the coefficient on the firm-specific risk measuresare less statistically significant.

Table 1

Regression of pay–performance sensitivity from financial wealth on firm total risk. Pay–performance

sensitivities are calculated as the dollar value change of chief executive officers’ total firm-specific financial

wealth (portfolio of firm stock and options) as a result of a $1,000 increase in shareholder value. The rank

of risk measures are percentage ranks that range from 0 (lowest risk) to 100 (highest risk). Year effects are

included in the regressions but are not reported. Three regressions are run: ordinary least squares (OLS),

median, and robust. Standard errors are reported in parentheses. Heteroskedasticity-robust standard

errors are reported for the OLS regression. The goodness-of-fit measures reported are either the adjusted

R-squared (OLS and robust regressions) or the pseudo R-squared (median regression). Asterisks indicate

significance at 5% (*) and 1% (**) levels. Sales, capital, research and development (R&D) expenditure,

advertising expenditure, and investment are in millions of dollars. All monetary variables are in 1994

constant dollars.

Variable Regression method

OLS regression Median regression Robust regression

Intercept 73.874** 60.506** 33.576**

(24.397) (2.991) (3.286)

Rank of total risk �0.505** �0.164** �0.113**(0.076) (0.007) (0.008)

Ln(sales) �4.499 �8.805** �2.838**(6.066) (0.772) (0.849)

[Ln(sales)]2 0.255 0.471** 0.109*

(0.332) (0.0487) (0.054)

Capital/sales �5.946 �0.996 �1.847**(3.156) (0.553) (0.608)

(Capital/sales)2 0.164 �0.021 0.349

(0.903) (0.188) (0.207)

R&D/capital 2.876 �1.145* �0.977(3.014) (0.507) (0.557)

Missing R&D 1.023 �0.568* �0.882**(1.983) (0.257) (0.282)

Advertising/capital 24.076* �0.446 �2.796**(10.491) (0.663) (0.755)

Missing advertising 4.420 �0.979** �1.562**(2.492) (0.336) (0.372)

Investment/capital �2.620 7.9020** 7.725**

(6.553) (0.947) (1.038)

Sample size 8177 8177 8177

Adjusted R2/pseudo R2 0.121 0.119 0.401


The economic significance of the result is large. Taking Table 3, for example, thepay–performance sensitivities estimated at the 25% level of firm-specific risk are55.278, 56.082, 29.282, and 57.220 for the OLS, median, robust, and instrumentalvariables regressions, respectively; those estimated at the 75% level, 29.707, 46.596,22.676, and 16.938, respectively, represent respective reductions of 46.3%, 16.9%,22.6%, and 70.4%. Estimates using other tables are comparable to those reportedhere. Because this study shows that systematic risk does not affect incentive levels, I

Table 2

Regression of pay–performance sensitivity from financial wealth on firm-specific risk. Pay–performance

sensitivities are calculated as the dollar value change of chief executive officers’ total firm-specific financial

wealth (portfolio of firm stock and options) as a result of a $1,000 increase in shareholder value. The rank

of risk measures are percentage ranks that range from 0 (lowest risk) to 100 (highest risk). Year effects are

included in the regressions but are not reported. Three regressions are reported: ordinary least squares

(OLS), median, and robust. Standard errors are reported in parentheses. Heteroskedasticity-robust

standard errors are reported for the OLS regression. The goodness-of-fit measures reported are either the

adjusted R-squared (OLS and robust regressions) or the pseudo R-squared (median regression). Asterisks

indicate significance at 5% (*) and 1% (**) levels. Sales, capital, research and development (R&D)

expenditure, advertising expenditure, and investment are in millions of dollars. All monetary variables are

in 1994 constant dollars.



Intercept 69.006** 59.760** 32.327**

(20.794) (2.940) (3.261)

Rank of total risk 0.297 0.000 �0.010(0.194) (0.027) (0.030)

Rank of firm-specific risk �0.843** �0.173** �0.109**(0.197) (0.028) (0.031)

Ln(sales) �3.086 �8.467** �2.545**(5.374) (0.760) (0.843)

[Ln(sales)]2 0.206 0.455** 0.097

(0.339) (0.048) (0.053)

Capital/sales �5.582 �0.531 �1.848**(3.841) (0.543) (0.602)

(Capital/sales)2 0.189 �0.129 0.371

(1.307) (0.184) (0.205)

R&D/capital 3.364 �1.030* �0.887(3.522) (0.498) (0.552)

Missing R&D 2.091 �0.443 �0.703*(1.801) (0.254) (0.282)

Advertising/capital 23.201** �0.553 �2.879**(4.775) (0.650) (0.749)

Missing advertising 4.119 �1.212** �1.533**(2.350) (0.329) (0.369)


(6.563) (0.929) (1.029)

Sample size 8177 8177 8177



also perform a regression in which I omit the term for systematic risk. The results areof qualitatively similar economic significance.All of the reported results suggest that firm-specific and systematic risk influence

pay–performance sensitivity differently. Firm-specific risk is clearly negativelyrelated to PPS even after controlling for systematic risk. The effect of systematic

Table 3

Regression of pay–performance sensitivity from financial wealth on systematic and firm-specific risk. Pay–

performance sensitivities are calculated as the dollar value change of chief executive officers’ total firm-

specific financial wealth (portfolio of firm stock and options) as a result of a $1,000 increase in shareholder

value. The rank of risk measures are percentage ranks that range from 0 (lowest risk) to 100 (highest risk).

Four regressions are reported: ordinary least squares (OLS), median, robust, and instrumental variable,

where the individual firms’ risk measures are used as independent variables and the risk measures

constructed from industry average percentage risk are used as the instrumental variables. Year effects are

included in the regressions but are not reported. Standard errors are reported in parentheses.

Heteroskedasticity-robust standard errors are reported for the OLS regression. The goodness-of-fit

measures reported are either the adjusted R-squared (OLS, robust, and instrumental variable regressions)

or the pseudo R-squared (median regression). Asterisks indicate significance at 5% (*) and 1% (**) levels.

Sales, capital, research and development (R&D) expenditure, advertising expenditure, and investment are

in millions of dollars. All monetary variables are in 1994 constant dollars.


OLS regression Median regression Robust regression IV regression

Intercept 68.064** 60.824** 32.585** 77.361**

(24.896) (3.001) (3.264) (21.170)

Rank of systematic risk �0.043 0.017 0.014 0.250

(0.189) (0.023) (0.025) (0.324)

Rank of firm-specific risk �0.511** �0.190** �0.132** �0.806**(0.192) (0.023) (0.026) (0.309)

Ln(sales) �2.958 �8.679** �2.606** �6.032(6.200) (0.775) (0.843) (5.463)

[Ln(sales)]2 0.207 0.466** 0.099 0.412

(0.336) (0.049) (0.053) (0.348)

Capital/sales �5.429 �0.580 �1.852** �2.115(3.211) (0.553) (0.602) (4.424)

(Capital/sales)2 0.135 �0.133 0.376 �0.550(0.909) (0.188) (0.205) (1.376)

R&D/capital 3.650 �1.067* �0.919 6.592

(3.094) (0.509) (0.553) (3.728)

Missing R&D 1.624 �0.449 �0.667* 1.541

(2.050) (0.259) (0.281) (1.834)

Advertising/capital 23.616* �0.583 �2.915** 24.909**

(10.327) (0.663) (0.749) (4.999)

Missing advertising 4.218 �1.208** �1.527** 4.198

(2.466) (0.336) (0.369) (2.441)

Investment/capital �1.476 7.976** 7.790** 3.356

(6.439) (0.947) (1.030) (6.883)

Sample size 8177 8177 8177 7815

Adjusted R2/pseudo R2 0.126 0.120 0.405 0.075


risk on PPS is ambiguous when controlling for firm-specific risk, consistent with theprediction of Model I in Section 2. Furthermore, for many specifications thecoefficient on systematic risk is insignificant after controlling for firm-specific risk,providing it some support for the prediction of Model II.

Table 4

Regression of pay–performance sensitivity from total wealth on systematic and firm-specific risk. Pay–

performance sensitivities are calculated as the dollar value change of chief executive officers’ total financial

wealth plus capitalized labor income as a result of a $1,000 increase in shareholder value. The rank of risk

measures are percentage ranks that range from 0 (lowest risk) to 100 (highest risk). Four regressions are

reported: ordinary least squares (OLS), median, robust, and instrumental variable, where the individual

firms’ risk measures are used as independent variables and the risk measures constructed from industry

average percentage risk are used as the instrumental variable. Year effects are included in the regressions

but are not reported. Standard errors are reported in parentheses. Heteroskedasticity-robust standard

errors are reported for the OLS regression. The goodness-of-fit measures reported are either the adjusted

R-squared (OLS, robust, and instrumental variable regressions) or the pseudo R-squared (median

regression). Asterisks indicate significance at 5% (*) and 1% (**) levels. Sales, capital, research and

development (R&D) expenditure, advertising expenditure, and investment are in millions of dollars. All

monetary variables are in 1994 constant dollars.



Intercept 70.319** 61.276** 37.956** 79.714**

(24.775) (3.761) (3.257) (21.110)

Rank of systematic risk �0.056 �0.017 0.011 0.226

(0.188) (0.029) (0.025) (0.323)

Rank of firm-specific risk �0.501** �0.159** �0.131** �0.786*(0.191) (0.029) (0.025) (0.308)

Ln(sales) �2.938 �8.272** �3.306** �6.047(6.170) (0.971) (0.841) (5.447)

[Ln(sales)]2 0.206 0.446** 0.140** 0.414

(0.334) (0.061) (0.053) (0.347)

Capital/sales �5.368 �1.063 �1.715** �2.152(3.219) (0.696) (0.603) (4.426)

(Capital/sales)2 0.108 �0.009 0.293 �0.565(0.911) (0.236) (0.205) (1.375)

R&D/capital 4.115 �0.264 �0.358 7.035

(3.088) (0.633) (0.551) (3.717)

Missing R&D 1.711 �0.289 �0.514 1.648

(2.046) (0.325) (0.281) (1.830)

Advertising/capital 23.461* �0.822 �3.199** 24.673*

(10.337) (0.865) (0.747) (4.986)

Missing advertising 3.938 �1.537** �1.853** 3.889

(2.471) (0.426) (0.368) (2.436)


(6.423) (1.189) (1.027) (6.864)

Sample size 7681 7681 7681 7343



4.2. Hypothesis testing

The above results show that the point estimates of the effects of systematic andnonsystematic risk on PPS are different. For comprehensiveness, I directly test tworelated hypotheses.

Table 5

Regression of pay–performance sensitivity from financial wealth on log systematic risk and log firm-

specific risk. Pay–performance sensitivities are calculated as the dollar value change of chief executive

officers’ total firm-specific financial wealth (portfolio of firm stock and options) as a result of a $1,000

increase in shareholder value. Log (systematic risk) is the natural log of the dollar systematic risk; log

(idiosyncratic risk), as the natural log of the dollar idiosyncratic risk. Four regressions are reported:

ordinary least squares (OLS), median, robust, and instrumental variable, where the individual firms’ risk

measures are used as independent variables and the risk measures constructed from industry average

percentage risk are used as the instrumental variable. Standard errors are reported in parentheses.

Heteroskedasticity-robust standard errors are reported for the OLS regression. The goodness-of-fit

measures reported are either the adjusted R-squared (OLS, robust, and instrumental variable regressions)

or the pseudo R-squared (median regression). Significance levels are indicated as follows: 1% (**), 5% (*),

10% (a), 20% (b). Sales, capital, research and development (R&D) expenditure, advertising expenditure,

and investment are in millions of dollars. All monetary variables are in 1994 constant dollars.



Intercept 127.850** 88.408** 50.180** 141.537**

(21.318) (2.751) (3.189) (26.984)

Log(systematic risk) �1.715 0.447a 0.294 �0.615(1.855) (0.230) (0.267) (3.096)

Log(firm-specific risk) �3.262a �1.841** �1.451** �5.047b

(1.961) (0.240) (0.279) (3.737)

Ln(sales) �14.789** �14.537** �6.028** �17.099**(5.342) (0.710) (0.823) (5.525)

[Ln(sales)]2 0.964** 0.824** 0.326 1.135**

(0.303) (0.046) (0.054) (0.364)

Capital/sales �5.646a �0.754b �1.588** �4.222(3.257) (0.527) (0.611) (4.571)

(Capital/sales)2 �0.078 �0.149 0.273b �0.458(0.928) (0.179) (0.208) (1.384)

R&D/capital 2.881 �0.938a �0.852b 5.666b

(3.094) (0.481) (0.560) (3.824)

Missing R&D 1.258 �0.659** �0.777** 1.433

(2.061) (0.246) (0.285) (1.821)

Advertising/capital 24.113* �0.678 �2.822** 24.170**

(10.566) (0.651) (0.757) (4.932)

Missing advertising 3.716b �1.242** �1.591** 3.300b

(2.508) (0.322) (0.373) (2.407)


(6.556) (0.900) (1.043) (6.964)

Sample size 8177 8177 8177 7815



1. To determine whether firm-specific risk and systematic risk have the same effecton pay–performance sensitivity, I test the hypothesis H0 : b1 ¼ b2 in Eq. (24).Note that for the hypothesis to make sense the measures of risk must be raw, notranked, measures.

2. Twenty-four regression models are checked.* Three regression methods (median, robust, and OLS).* Four measures of risk, three estimated using the market model regression (60

monthly data, one year of weekly data, and three years of weekly data) andone using the Fama-French model regression.

* PPS from total wealth change and financial wealth change, respectively.

In all regressions, I control for firm size and the productivity of CEO effort usingthe control variables discussed above. Eighteen of the regression models reject H0 atthe 1% significance level, 22 reject H0 at the 5% significance level.

1. To determine whether there is extra explanatory power by adding the term of therank of firm-specific risk, after controlling for rank of total risk. I test thehypothesis: H0 : b2 ¼ 0 in the regression

PPS ¼ aþ b1Total Risk þ b2Firm Specific Risk


Of the same 24 regression models that I check, 22 reject H0 at the 1 significancelevel, the remaining two reject H0 at the 5% level.

4.3. Subsample study

The argument in Section 2.2 assumes that CEOs can fully adjust their exposure tomarket risk by trading the market portfolio. But because there exist constraints ontrading, CEOs might obtain too large an exposure to the market risk and be unableto fully adjust through trading. This leads to the prediction that the relation betweensystematic risk and CEOs’ PPS will differ with the size of their equity holdings intheir firms. CEOs with small holdings in their firms’ equity can relatively easilyoptimize the systematic risk they incur; hence, systematic risk should not affect theirPPS. CEOs with large holdings in their firms’ equity might not be able to fully adjusttheir systematic risk. Particularly, if their firm equity holdings incur more than theoptimal exposure to systematic risk, their cost of bearing systematic risk should behigher and their PPS should decrease with that systematic risk, as predicted inSection 2.3.1.To test this prediction, I divide the data into two subsamples, one with above-

median total dollar equity holdings in the firm and the other with below-median totaldollar equity holdings in the firm, and run the regression in Table 3 on both.The results are reported in Table 6. Across three regression methods (OLS,

median, and robust) and both subsamples, the firm-specific risk measure is alwaysnegatively related to PPS. The systematic risk measure exhibits a different pattern foreach subsample. For CEOs with above-median holdings in their firms’ equity, the


Table 6

Subsample analysis of the regression of pay–performance sensitivity on the systematic and firm-specific

risk. Panel A reports the regression analysis for the subsample of chief executive officers (CEOs) whose

stock and options holdings in their firms are above the median level of the sample. Panel B reports the

regression analysis for the subsample of CEOs whose stocks and options holdings in their firms are below

the median level of the sample. Pay–performance sensitivities are calculated as the dollar value change of

CEOs’ total firm-specific financial wealth (portfolio of firm stock and options) as a result of a $1,000

increase in shareholder value. The rank of risk measures are percentage ranks that range from 0 (lowest

risk) to 100 (highest risk). Year effects are included in the regressions but are not reported. Standard errors

are reported in parentheses. Heteroskedasticity-robust standard errors are reported for the ordinary least

squares (OLS) regression. The goodness-of-fit measures reported are either the adjusted R-squared (OLS

and robust regressions) or the pseudo R-squared (median regression). Asterisks indicate significance at 5%

(*) and 1% (**) levels. Sales, capital, research and development (R&D) expenditure, advertising

expenditure, and investment are in millions of dollars. All monetary variables are in 1994 constant dollars.



Panel A. CEOs with above median holdings in their firms’ equity

Intercept 131.100** 147.570** 116.669**

(42.953) (8.483) (5.967)

Rank of systematic risk �0.460 �0.295** �0.183**(0.413) (0.074) (0.052)

Rank of firm-specific risk �0.980* �0.292** �0.186**(0.423) (0.075) (0.053)

Ln(sales) �3.771 �20.748** �16.550**(10.875) (2.152) (1.515)

[Ln(sales)]2 0.484 1.195** 0.911**

(0.586) (0.132) (0.093)

Capital/sales �0.651 1.007 0.295

(6.163) (1.624) (1.152)

(Capital/sales)2 �1.638 �1.069* �0.527(1.678) (0.536) (0.382)

R&D/capital 7.598 1.341 0.478

(4.300) (1.194) (0.838)

Missing R&D 5.069 0.630 �0.183(3.148) (0.692) (0.487)

Advertising/capital 48.317** 11.414** �0.539(10.437) (1.763) (1.236)

Missing advertising 14.626** 2.012** �0.844(3.078) (0.839) (0.590)

Investment/capital �19.791* �1.435 0.737

(9.984) (2.530) (1.788)

Sample size 4088 4088 4088


Panel B. CEOs with below median holdings in their firms’ equity

Intercept 74.515** 47.063** 32.414**

(9.715) (3.289) (2.836)

Rank of systematic risk �0.005 �0.018 �0.017(0.040) (0.022) (0.019)

Rank of firm-specific risk �0.313** �0.159** �0.132**


coefficient on systematic risk is significantly negative for both median and robustregressions and negative, albeit not significantly, for the OLS regression. Forexample, in the first column of Table 6, Panel A, in the OLS regression, thecoefficient on rank of systematic risk is �0.460, with a standard error of 0.413, andthe coefficient on rank of firm-specific risk is �0.980, with a standard deviation of0.423. This lends some support to the notion that incentive contracts will differdepending on whether CEOs can easily hedge their market risk component.Systematic risk could also negatively affect the PPS of CEOs with large holdings intheir firms’ equity, although the influence of systematic and nonsystematic risk mightbe different. Systematic risk does not seem to affect the incentive level of CEOs withsmall holdings in their firms’ equity.The categorization according to total dollar holdings in firm equity can be

improved. Depending on firms’ beta and the delta of the options, the same dollarholdings could imply different exposure to systematic risk. As a robustness check, Irepeat the subsample study using dollar exposure to systematic risk instead of dollarexposure to firm equity. The results, omitted for brevity, are similar to those reportedin Table 6.These subsample study results are consistent with Garvey and Milbourn (2001) in

contemporaneous work, that market risk does matter for incentives when CEOs areyounger and less wealthy, thus more likely constrained in their ability to hedge themarket exposure in their compensation package. The two papers show from different

Table 6 (continued)



(0.055) (0.022) (0.019)

Ln(sales) �11.559** �7.450** �4.206**(2.440) (0.869) (0.751)

[Ln(sales)]2 0.790** 0.481** 0.269

(0.152) (0.057) (0.050)

Capital/sales �2.484** �1.696** �1.819**(0.871) (0.555) (0.478)

(Capital/sales)2 0.403 0.432* 0.377*

(0.342) (0.192) (0.166)

R&D/capital �1.209 �0.037 0.330

(1.350) (0.690) (0.611)

Missing R&D �1.676 �0.347 �0.325(0.884) (0.286) (0.245)

Advertising/capital �2.949** �1.639* �0.791(1.133) (0.794) (0.684)

Missing advertising �1.730* �0.387 0.127

(0.811) (0.415) (0.356)


(3.110) (1.028) (0.893)

Sample size 4089 4089 4089



angle that managerial constraints in hedging the market risk will lead to a bigger roleof the market risk in compensation contracts.

5. Robustness of the results

This subsection discusses the robustness of the results reported in this paper.I discuss three categories of robustness checks: robustness of the measure ofpay–performance sensitivity, robustness of the measures of risk, and otherexplanations that might drive the results.

5.1. Robustness of the measure of pay–performance sensitivity

I discuss three robustness checks on the measure of pay–performance sensitivities.

5.1.1. Relative performance versus total performance

The standard definition of pay–performance sensitivity is as a measure of thechange in CEO wealth as a result of the total performance of stock, which includesboth market and relative performance components. Alternatively, I can measureCEO pay change as a function of the relative performance of the firm. As Murphy(1985) reports, it does not seem to matter whether the raw return or relativeperformance return is used, as long as the two are not used simultaneously. I alsodefine a refined measure of pay–performance sensitivity using the relativeperformance measure to perform the analysis. The results do not changequalitatively.

5.1.2. Adjustment for CEO valuation of stock and options package

The conventional approach to valuing CEO stock and options packages used inthe construction of pay–performance sensitivity measures is likely to exaggerate thevalue of CEOs’ financial wealth. Because of inefficient risk bearing, CEOs who find itcostly to bear the firm-specific risk embedded in their firms’ stocks and options valuethese stocks and options at less than the market valuation. Hall and Murphy (2002),Kahl et al. (2002), and Meulbroek (2001) directly address the issue of CEOs’ lack ofdiversification, and Detemple and Sundaresan (1999) discuss the impact of tradingrestrictions in the underlying assets on the optimal exercising strategy and valuationof American options. As a robustness check, I estimate CEOs’ valuation of theirstock and options portfolios following Meulbroek (2001) and reestimate the pay–performance sensitivity measures accordingly. Performing a regression analysis toassess the relation between this revised measure of pay–performance sensitivity andthe measures of systematic and nonsystematic risk yields similar results.

5.1.3. Subsample of firms with full options data

I employ the ExecuComp data to estimate CEO compensation. A limitation of thedata set is the lack of precise exercise price information for out-of-money options,


which could render imprecise pay–performance sensitivity calculated for CEOs withsuch options.Because CEO stock options are typically granted for 10 years and at the money, if

the current stock price is higher than the stock prices in any of the previous 10 years,the previous year options grants are all in-the-money and there is no miscalculationof the options exercise price. For this reason, I construct a subsample in which thecurrent stock price is higher than the stock prices in any of the previous 10 years(after adjusting for stock split, but not for dividend, executive stock options typicallynot being protected for dividend). The effect for this subsample is similar to the fullsample result. However, the approach creates a sample selection bias, in that for onlyabout 45% of the firm-year observations is the current year stock price higher thanthe previous 10 years’ stock prices, and these firms are likely to be the outperformers.Thus, by focusing on this subsample I could unintentionally pick up characteristicsthat belong to the outperformers.In the United Kingdom, where companies are asked (but not required) to disclose

the full-information option history of every grant, it is possible to construct theactual PPS and compare it with the limited information estimate of PPS based ondisclosed grant information. Conyon and Sadler (2002), who compare the twomethodologies using data from the United Kingdom, find essentially no difference inthe PPS estimated using the full-information and limited-information data.

5.2. Robustness of the measures of risk

I supplement the market model regression decomposition of risk with several otherapproaches.First, I use a Fama-French three-factor model, shown by empirical asset pricing

literature to be superior to the market model in capturing the systematic (priced)risk, to decompose total risk into systematic and firm-specific risk. Given that in mytheory model (Section 2.1) the ambiguity of the impact of systematic risk on PPSderives from the fact that this systematic risk is priced by both the stock market andCEOs, the three-factor model might yield a more sensible measure of the truesystematic risk in the present setting. The results I obtain using these alternativemeasures of risk are qualitatively similar to those reported in the paper.Second, in response to the criticism that a market model regression might

introduce a large measurement error, I adopt a regression-free approach as proposedby Campbell et al. (2000) that estimates the industry average level of risk withoutestimating betas in a market model. The Campbell et al. approach provides analternative measure of the risk. Detailed procedures for getting the Campbell et al.measures can be obtained from the author. The results yielded by this alternativemeasure of risk are qualitatively similar to those reported in the paper.Third, again in response to the criticism that firms’ systematic risk might be

estimated inaccurately, I perform the regression analysis with risks constructed usingthree different combinations of data frequency and horizon: five years of monthlydata, one year of weekly data, and three years of weekly data. The results are notsensitive to these different risk measures. I also perform a regression in which I use


the systematic risk estimated from monthly regressions as the independent variableand the systematic risk estimated from three years of weekly data as an instrumentalvariable. The results are qualitatively similar to those reported in the paper.

5.3. Are other factors driving the results?

I consider the following factors to see whether the observed results can be mainlydriven by them.

5.3.1. Subsample of firms with positive dividends

If I credit the hypothesis that firms with severe cash constraints might emphasizerestricted stock and options over cash compensation such as salary and bonuses, ahigher pay–performance sensitivity might be attributable to the cash constraint. Oneway reported in the literature to address the cash constraint issue is to assume thatcash-constrained firms do not pay dividends. Of 9,714 firm-year observations, 6,261,or roughly two-thirds, have positive dividend payments. I therefore construct asubsample with positive dividends and assume that, at least for this subsample, thecash constraint is not severe. The results are similar to those reported in the paper.

5.3.2. Controlling for size effect

In Section 3, in discussing the measurement of variables, I explain why the knowneffect of size on PPS should be carefully controlled. In addition, it could be arguedthat, because the job of controlling large firms is too complicated to be handled by asingle manager, the role of CEO is to some extent played by the top managementteam. Thus, the CEO might be taking a lesser responsibility and lesser share in firmperformance and the management team a comparably greater responsibility. TheExecuComp database reports the compensation of the five most highly paidexecutives in the firm in each year, which can be used to construct a proxy of thetotal pay–performance sensitivity of the management team. This measure is likely tobe more robust than measures for individual CEOs to size-related heterogeneity inpay–performance sensitivities. Repeating the empirical analysis using the pay–performance sensitivity for the management team yields qualitatively similar results.

5.3.3. Convertibility of securities and dilution effect

The main analysis implicitly assumes that a company has a fixed amount of equityoutstanding. Thus, pay–performance sensitivities can be interpreted as theproportion of the total outstanding equity held by the CEO. But the existence ofconvertible securities can complicate matters. When a firm does well, manyconvertible securities might be converted into equity, which implies that CEOpay–performance sensitivity could be lower on the upside and higher on thedownside.Because COMPUSTAT does not provide exact terms of conversion, the issue of

convertibility can be addressed only approximately. One useful measure is the bookvalue of convertible securities as a percentage of the sum of book value of equity and


book value of convertible securities. If that measure is large, the convertibility ofsecurities might have a significant impact on pay–performance sensitivities. The dataset I use records a measure higher than 10% for less than 10% of the firm-yearobservations. If the measure is defined as the ratio of total book value of convertiblesecurities over the sum of market value of equity and book value of convertiblesecurities, less than 5% of the firm-year observations would have a measure higherthan 10%. Therefore, generally speaking, the effect of dilution is not large.As a robustness check I construct a modified measure of CEO pay–performance

sensitivity in which I treat convertible securities as if they were common stocks.Using this modified measure of CEO pay–performance sensitivity in the regressionanalysis yields qualitatively similar results.However, in many companies the primary source of potential dilution might be

employee stock options. Consequently, what I propose here only partially resolvesthe problem, and better data on the employee stock options will enable us to moreaccurately estimate the impact of dilution.

5.3.4. The impact of stock option resetting on pay–performance sensitivity

In practice, firms sometimes reset stock options after a severe underperformance.It is helpful to know what effect this might have on the foregoing analysis.Intuitively, option resetting will decrease the ex-ante incentive because CEOs will

build in the expectation that the effects of poor performance will be partially offsetby a windfall provided through resetting. The effect, however, is small, as shown byBrenner et al. (2000).The probability of option resetting increases with the degree of underperformance.

Taking 1995, for example, 75% of firms in ExecuComp have returns of 2% orhigher. According to Brenner et al. (2000), the likelihood of resetting at thatperformance level is only about 1%. More than 90% firms perform at �20% orbetter, and the probability of resetting at �20% performance is about 12%. In theevent of resetting, observe Brenner et al. (2000), the value of CEO options increasesby about 40%. Thus, the ex-ante value change due to resetting is probably less than1%, which has at most a negligible effect on ex-ante CEO incentives.

5.3.5. The impact of past return on current period pay–performance sensitivity

Another concern that might be raised is whether a relation could exist betweenpast stock return and current period pay–performance sensitivity. For example,might firms that suffer adverse shocks in previous years decrease pay–performancesensitivity to protect their CEOs from further underperformance? If so, and if pastreturn is negatively related to current level of firm-specific risk, then what I ampicking up might be the fact that compensation plans do not have much sensitivityon the downside.In the data, the correlation between past return and current period pay–

performance sensitivity is slightly negative (�0.04), which would suggest that poorlyperforming firms have slightly higher pay–performance sensitivity. Moreover, when Ilimit the sample to firms with negative returns over the previous year, the correlationbetween past return and current period pay–performance sensitivity is more


negative, suggesting that very poorly performing firms’ pay–performance sensitivityis much higher. A direct comparison of pay–performance sensitivity levels for theentire sample and the decile of firms with the lowest return last year (which could beconstrued to be distressed firms) reveals mean (median) pay–performance sensitivityto be 29.0 (12.7) for the entire sample and 50.6 (26.3) for distressed firms. Distressedfirms thus seem to have much higher pay–performance sensitivity than other firms.This finding is reasonable if the other side of the trade-off is also considered; that is,if distressed firms are more dependent on CEO effort, the productivity of CEOeffort could be higher, which implies that pay–performance sensitivity should behigher.

6. Conclusion

This paper generates two important insights regarding the connection betweenCEO incentives and firm risk. First, when CEOs cannot trade the market portfolio,incentive is ambiguously related to firms’ systematic risk because CEOs do notalways have a disadvantage relative to representative investors in bearing that risk.Second, when CEOs can trade the market portfolio, systematic risk has no bearingon incentive level, because CEOs can adjust their holdings such that the cost ofbearing the systematic risk is the same as for investors. Incentive level alwaysdecreases, however, with firm-specific risk.I design empirical tests to investigate the predictions of these models. Using a

variety of risk measures and regression methods, I demonstrate that a robust relationexists between firm-specific risk and incentive level and no robust relation existsbetween a firm’s systematic risk and incentive level. Subsample analyses reveal thatthe incentives of CEOs who are less likely to be constrained from trading the marketportfolio do not seem to change with their firms’ systematic risk, whereas theincentives of CEOs who are likely to face a binding constraint on short-selling themarket portfolio seem to decrease with both systematic and firm-specific risk. Thesefindings are consistent with the predictions of theory under the assumption thatCEOs can adjust to some extent their exposure to market risk.

Appendix A

A.1. Proof of Eqs. (8)–(10)

For the problem represented by Eqs. (5)–(7), I can write the Lagrangine

L ¼ð1� bÞ½ðX0 þ keÞ � Zðrm � rf Þ� � s

þ l bðX0 þ keÞ þ s � f ðeÞ �1

2b2gAðZ

2s2m þ s2dÞ � CEA

� �þ m bk � f 0ðeÞ

� �:

ðA:1Þ


The first-order conditions are, with respect to b; s; e; l; and m;

�½ðX0 þ keÞ � Zð%rm � rf Þ� þ lðX0 þ keÞ � blgAðZ2s2m þ s2dÞ þ mk ¼ 0; ðA:2Þ

�1þ l ¼ 0; or l ¼ 1; ðA:3Þ

ð1� bÞk þ lbk � lf 0ðeÞ � mf 00ðeÞ ¼ 0; ðA:4Þ

½bðX0 � keÞ þ s � f ðeÞ� �1

2b2gA Z2s2m þ s2d

� �¼ CEA; ðA:5Þ

and

f 0ðeÞ ¼ bk: ðA:6Þ

Incorporating Eq. (A.6) into Eq. (A.4) and simplifying I get

ð1� bÞk � mf 00ðeÞ ¼ 0; ðA:7Þ

which gives m as a function of other parameters:

m ¼ð1� bÞk

f 00ðeÞ: ðA:8Þ

This has a clean interpretation. Eq. (A.4) gives the trade-off in increasing effort level.On the positive side, a higher effort will bring extra benefit to the principal, which isignored in the design of the agent’s own effort level trade-off. On the negative side, itinduces the agent to work harder and thus incur the increasing cost of effort,captured by the curvature of the f ðeÞ function.Eq. (A.8) gives the shadow price of the incentive compatibility constraint, which is

the ratio of the extra benefit to the principal over the measure of the increased cost tothe agent.Combining Eqs. (A.3) and (A.2) results in

Zðrm � rf Þ � bgAðZ2s2m þ s2dÞ þ mk ¼ 0: ðA:9Þ

Here, higher incentive (an increase in b) will

* reduce the cost to the principal (or market) of bearing systematic risk byZðrm � rf Þ on the margin, which is good for the principal;

* increase the agent’s cost of bearing risk by bgAðZ2s2m þ s2dÞ on the margin, which is

bad for the principal, who must increase the s term to make up the reservationutility for the agent; and

* incentivize the agent to work harder and loosen the incentive compatibilityconstraint. The benefit of this is captured by the shadow price of the ICconstraint, m; and the productivity of effort on firm performance, k:

Combining Eqs. (A.9) and (A.8) and reorganizing the terms yields the result forb : The equations for e and s are implicitly determined once b is determined.


A.2. Proof of Eqs. (19)–(21)

The Lagrangine can be written as

L ¼ ð1� bÞ½X0 þ ke � Zðrm � rf Þ� � s þ lIR þ m bk � f 0ðeÞ� �

; ðA:10Þ

where

IR ¼ b½X0 þ ke � Zðrm � rf Þ� þ s � f ðeÞ þ1

2

ðrm � rf Þ2

gAs2m�1

2gAb2s2d � CEA:

The first-order conditions are, with respect to b; s; e; l; and m;

�ðX0 þ keÞ þ Zðrm � rf Þ þ l½X0 þ ke � Zðrm � rf Þ� � blgAs2d þ mk ¼ 0; ðA:11Þ

�1þ l ¼ 0; or l ¼ 1; ðA:12Þ

ð1� bÞk þ lbk � lf 0ðeÞ � mf 00ðeÞ ¼ 0; ðA:13Þ

b½ %X � Zðrm � rf Þ� þ s � f ðeÞ þ1

2

ðrm � rf Þ2

gAs2m�1

2gAb2s2d ¼ CEA; ðA:14Þ

and

f 0ðeÞ ¼ bk: ðA:15Þ

Incorporating Eqs. (A.15) into (A.13) and simplifying, I get

ð1� bÞk � mf 00ðeÞ ¼ 0; ðA:16Þ

which gives m as a function of other parameters

m ¼ð1� bÞk

f 00ðeÞ: ðA:17Þ

Combining Eqs. (A.12) and (A.11) results in

bgAs2d ¼ mk: ðA:18Þ

Combining the last two equations yields the result for b: The equations for e and s

are implicitly determined once b is determined.

A.3. Measuring pay–performance sensitivity

This discussion closely follows the discussions in Jensen and Murphy (1990) andHall and Liebman (1998). Two components of CEO wealth are influenced by firmperformance: capitalized future labor income and financial capital. The changes inthese components can be measured by total direct compensation and re-evaluationof stock and options holdings, respectively. Total direct compensationincludes salary and bonuses, plus the value of any new grants in stock, options,long-term incentive compensation, and others that CEOs receive in a given period.Regarding reevaluation of stock and stock options holdings, CEOs often have large


holdings of stock and stock options, the value of which changes with firmperformance.

A.3.1. Total direct compensation change

As Jensen and Murphy (1990) point out, two different assumptions can be madeabout how firm performance affects total direct compensation. The first,conservative, assumption is that firm performance affects only the current period’stotal direct compensation and has no influence on future compensation levels. If thisis so, I can add total direct compensation from the current period to the change inCEO stock and options value due to reevaluation to calculate total change in CEOwealth.The second assumption is that performance has a permanent effect on total direct

compensation, that good firm performance in the current period increases not onlyCEOs’ current, but also their future, pay. Under this assumption of a lingering effecton CEO pay, I compute the present value of the changes in future compensation cashflows as a result of this year’s performance. Consistent with Jensen and Murphy(1990), I first use a regression to estimate the effect of firm performance on thecurrent and next period pay change, then calculate the present value of the CEO’sdirect compensation cash flow by making certain assumptions about interest rateand retirement age.The assumption that firm performance influences only current period direct

compensation may be too conservative; the assumption that it permanently affectsCEO pay could be too strong. Jensen and Murphy (1990) caution that suchtreatment might exaggerate the effect of performance on pay. For one thing, thebonus component of direct compensation is likely to be transitory. The truth likelylies somewhere in between. Thus, I calculate the two as lower bound and upperbound, respectively, and test both in my regression analysis. There is little change inthe results. The results reported in Table 4 are calculated under the assumption thatperformance affects pay permanently.

A.3.2. Reevaluation of stock and stock options

CEOs typically hold a fair amount of their firms’ stock and stock options.Reevaluation of these financial assets contingent on firm performance can causemajor changes in CEO wealth. Hall and Liebman (1998) conclude that thereevaluation effect dwarfs the change in total direct compensation in terms ofproviding incentive.To calculate the magnitude of CEO wealth change due to reevaluation of stock

and stock options, I need to know the amount of stock holdings; the amount, strikeprice, and maturity of options; and other parameters that affect option value such asvolatility of stock, dividend yield, riskless interest rate, and current stock price. Mydata set has full information about stock holdings, but some information aboutoption holdings is missing and must therefore be approximated.


The ExecuComp data set, like most of the other data sets used in thecompensation analysis, has complete information only for the current year optionsgrant. The data set divides previous years’ options grants into exercisable andunexercisable options and reports for each category the amount of options andintrinsic value of in-the-money options (the latter is defined as the payoff fromexercising the option immediately). To get full information about holdings ofoptions granted in previous years, some assumptions need to be made and theoptions holdings must be estimated. Murphy (1999) and Hall and Liebman (1998)both provide estimation methods. I use the method developed by Core and Guay(1999), which is similar to the Hall and Liebman (1998) approach. Core and Guay(1999) show that their method yields estimates of option portfolio sensitivities thatare effectively unbiased and 99% correlated with the measures that would beobtained if the parameters of a CEO’s option portfolio were known.To calculate the hypothetical increase in CEO financial wealth due to a $1,000

increase in shareholder value, I first calculate the change in CEO financialwealth when firm return increases from the median return of the market to 1%above the median return. I divide this number by the change in total shareholdervalue attributable to the 1% increase in firm return and multiply the result by1,000.I differ from the existing literature in the calculation of the sensitivity

of an option’s value to stock price. Many investigators use the option’s d (hedgeratio) to measure pay–performance sensitivity. Although roughly correct, thisapproach fails to consider the time value of options. If the stock price over the yearincreases by $1, the value of any options that a CEO holds at the beginningof the year does not increase by $d because there is shortening by one year of theoption’s maturity. In fact, if the stock price increase is small, the option value candecrease. My measure is typically lower than that calculated using the option hedgeratio.CEO wealth change due to options is added to CEO wealth change due to

stock to arrive at total CEO wealth change due to reevaluation of stock and options.This value is then added to CEO capitalized future labor income changeto obtain total CEO wealth change due to firm performance. Following Jensenand Murphy (1990), I measure pay–performance sensitivity as the change inCEO total wealth for a $1,000 increase in firm value. In the regression analysis,all measures of pay–performance sensitivity are calculated using 1994 constantdollars.

A.3.3. Truncating the outliers

The raw measures of pay–performance sensitivity are highly skewed and fat-tailedas a consequence of outliers. In subsequent analyses, I employ a truncated measurewhereby I replace the top and bottom 1% of the data with the 99th percentile and 1stpercentile values, respectively.


References

Aggarwal, R., Samwick, A., 1999. The other side of the trade-off: the impact of risk on executive

compensation. Journal of Political Economy 107, 65–105.

Aggarwal, R., Samwick, A., 2001. Why do managers diversify their firms? Agency reconsidered.

Unpublished working paper, Dartmouth College.

Baker, G., Hall, B., 1998. CEO incentives and firm size. NBER working paper 6868, National Bureau of

Economic Research, Cambridge, MA.

Berk, J., 1995. A critique of size-related anomalies. Review of Financial Studies 8, 275–286.

Bertrand, M., Mullainathan, S., 2000. Agents with and without principals. American Economic Review

90, 203–208.

Bettis, J., Bizjak, J., Lemmon, M., 2001. Managerial ownership, incentive contracting, and the use of zero-

cost collars and equity swaps by corporate insiders. Journal of Financial and Quantitative Analysis 36,

345–370.

Brenner, M., Sundaram, R., Yermack, D., 2000. Altering the terms of executive stock options. Journal of

Financial Economics 57, 103–128.

Campbell, J., Lettau, M., Malkiel, B., Xu, Y., 2000. Have individual stocks become more volatile? an

empirical exploration of idiosyncratic risk. Journal of Finance 56, 1–43.

Carpenter, J., 1998. The exercise and valuation of executive stock options. Journal of Financial Economics

96, 453–473.

Conyon, M., Sadler, G., 2002. CEO compensation, option incentives and information disclosure. Review

of Financial Economics 10, 251–277.

Core, J., Guay, W., 1999. The use of equity grants to manage optimal equity incentive levels. Journal of

Accounting and Economics 28, 151–184.

Core, J., Guay, W., 2002. The other side of the trade-off: the impact of risk on executive compensation; a

comment. Journal of Political Economy, forthcoming.

Coughlan, T., Schmidt, R., 1985. Executive compensation, management turnover, and firm performance:

an empirical investigation. Journal of Accounting and Economics 7, 43–66.

Dammon, R., Spatt, C., Zhang, H., 2000. Diversification and capital gains taxes with multiple risky assets.

Unpublished working paper. Carnegie Mellon University.

Demsetz, H., Lehn, K., 1985. The structure of corporate ownership: causes and consequences. Journal of

Political Economy 93, 1155–1177.

Detemple, J., Sundaresan, S., 1999. Nontraded asset valuation with portfolio constraints: a binomial

approach. Review of Financial Studies 12, 835–872.

Fama, E., French, K., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427–465.

Fama, E., MacBeth, J., 1973. Risk, return and equilibrium: empirical tests. Journal of Political Economy

81, 607–636.

Garen, J., 1994. Executive-compensation and principal–agent theory. Journal of Political Economy 102,

1175–1199.

Garvey, G., Milbourn, T., 2001. The RPE puzzle: the answer lies in the cross-section. Unpublished

working paper. Washington University in St. Louis.

Gibbons, R., 1998. Incentives in organizations. Journal of Economic Perspective 12, 115–132.

Gibbons, R., Murphy, K., 1992. Optimal incentive contracts in the presence of career concerns: theory and

evidence. Journal of Political Economy 100, 468–505.

Greene, W., 1993. Econometric Analysis. Macmillan Publishing Company, New York.

Hall, J., Liebman, J., 1998. Are CEOs really paid like bureaucrats? Quarterly Journal of Economics 113,

653–691.

Hall, B.J., Murphy, K.J., 2002. Stock options for undiversified executives. Journal of Accounting and

Economics, 33, 3–42.

Himmelberg, C., Hubbard, G., Palia, D., 1999. Understanding the determinants of managerial

ownership and the link between ownership and performance. Journal of Financial Economics 53,

353–384.

Holmstrom, B., 1979. Moral hazard and observability. Bell Journal of Economics 10, 74–91.


Holmstrom, B., 1999. Managerial incentive problems: a dynamic perspective. Review of Economic Studies

66, 169–182.

Holmstrom, B., Milgrom, P., 1987. Aggregation and linearity in the provision of intertemporal incentives.

Econometrica 55, 303–328.

Holmstrom, B., Milgrom, P., 1991. Multi-task principal agent analysis: linear contracts, asset ownership

and job design. Journal of Law, Economics, and Organization 7, 24–52.

Hubbard, R., Palia, D., 1995. Executive pay and performance: evidence from the US banking industry.

Journal of Financial Economics 39, 105–130.

Jensen, M., Meckling, W., 1976. Theory of firm: managerial behavior, agency costs and ownership

structure. Journal of Financial Economics 3, 305–360.

Jensen, M., Murphy, K., 1990. Performance pay and top management incentives. Journal of Political

Economy 98, 225–264.

Jin, L., 2001. Essays in financial economics. Ph.D. dissertation. Massachusetts Institute of Technology.

Kahl, M., Liu, J., Longstaff, F., 2002. Paper millionaires: how valuable is stock to a shareholder who is

restricted from selling it? Journal of Financial Economics, forthcoming.

Koenker, R., Bassett, G., 1982. Robust tests for heteroscedasticity based on regression quantiles.

Econometrica 50, 43–61.

Kraft, K., Niederprum, A., 1999. Determinants of management compensation with risk-averse agents and

dispersed ownership of the firm. Journal of Economic Behavior and Organization 40, 17–27.

Lambert, R., Larcker, D., 1987. An analysis of the use of accounting and market measures of performance

in executive compensation contracts. Journal of Accounting Research 25, 85–125.

Meulbroek, L., 2000. Does risk matter? Corporate insider transactions in Internet-based firms.

Unpublished working paper 00-062. Harvard Business School.

Meulbroek, L., 2001. The efficiency of equity-linked compensation: understanding the full cost of

awarding executive stock options. Financial Management 30, 5–30.

Murphy, K., 1985. Corporate performance and managerial remuneration. Journal of Accounting and

Economics 7, 11–42.

Murphy, K., 1986. Incentives, learning and compensation: a theoretical and empirical investigation of

managerial labor contracts. Rand Journal of Economics 17, 59–76.

Murphy, K., 1999. Executive compensation. In: Ashenfelter, O., Card, D. (Eds.), Handbook of Labor

Economics., Vol. 3. North-Holland, Amsterdam, pp. 2485–2563.

Ofek, E., Yermack, D., 2000. Taking stock: does equity-based compensation increase managers

ownership. Journal of Finance 55, 1367–1384.

Prendergast, C., 2002. The tenuous trade-off of risk and incentives. Journal of Political Economy,

Forthcoming.

Schaefer, S., 1998. The dependence of pay–performance sensitivity on the size of the firm. Review of

Economics and Statics 3, 436–443.

Schizer, D., 2000. Executives and hedging: the fragile legal foundation of incentive compatibility.

Columbia Law Review 100, 440–504.

Smith, C., Watts, R., 1992. The investment opportunity set and corporate financing, dividend, and

compensation policies. Journal of Financial Economics 3, 263–292.

Street, J., Carroll, R., Ruppert, D., 1988. A note on computing robust regression estimates via iteratively

reweighed least squares. American Statistician 42, 152–154.

Yermack, D., 1995. Do corporations award CEOs stock-options effectively? Journal of Financial

Economics 39, 237–269.


Documents

CEO compensation, diversification, and incentives