An Empirical Analysis of the Role of Risk Aversion. in Executive Compensation Contracts. Frank Moers. and. Erik Peek

Transcription

1 An Empirical Analysis o the Role o Risk Aversion in Executive Compensation Contracts Frank Moers and Erik Peek Maastricht University Faculty o Economics and Business Administration MARC / Department o Accounting and Auditing P.O. Box MD Maastricht The Netherlands MARC Working Paper MARC-WP/3/000-07

2 An Empirical Analysis o the Role o Risk Aversion in Executive Compensation Contracts Abstract. This paper empirically tests the principal-agent model prediction that the use o perormance measures or incentive purposes is aected by the agent s risk aversion. We ind that the use o both accounting and market perormance measures in executive compensation contracts decreases as the level o risk aversions increases. We urther ind that agent-speciic characteristics, i.e., risk aversion, become more important in designing executive compensation contracts when perormance measures are less useul due to measure-speciic characteristics. Key Words: Risk aversion, agency theory, executive compensation. 1

3 The use o accounting and market perormance measures in executive compensation contracts has received considerable attention in the accounting literature. Agency theory predicts that in order to provide incentives, management compensation should be linked to measures o perormance that are inormative about the eort provided by managers (Holmström, 1979). Analytical studies in accounting indicate that both accounting and market perormance measures are inormative and should thereore be used or incentive purposes (e.g., Bushman and Indjejikian, 1993; Feltham and Xie, 1994). These studies urther show that the incentive weight o a perormance measure depends on measure-speciic characteristics and agentspeciic characteristics (e.g., Banker and Datar, 1989; Bushman and Indjejikian, 1993) The empirical accounting literature has tried to examine to what extent the agency theory predictions can explain observed practices. This research shows that CEO compensation is on average related to both accounting perormance and stock perormance (e.g., Lambert and Larcker, 1987; Sloan, 1993; Baber et al., 1999). Furthermore, studies that aim to explain the cross-sectional dierences in the use o perormance measures, ind that the use o accounting perormance measures decreases relative to the use o market perormance measures when its relative noise increases (e.g., Lambert and Larcker, 1987) and when the irm s growth opportunities increase (e.g., Lambert and Larcker, 1987; Baber et al., 1996). In general, these studies ocus on irm characteristics (measure-speciic characteristics) o which agency theory predicts that these aect the use o perormance measures in compensation contracts. However, agency theory also predicts that the use o perormance measures depends on agent-speciic characteristics, i.e. the risk aversion o the agent. However, no attempt has been made so ar to empirically examine the eect o risk aversion on the use o perormance measures or incentive purposes. The relationship between risk aversion and the use o perormance measures in compensation contracts is especially relevant at the CEO level where contracts are more

4 tailor-made. Discussions in the economics literature indicate that the assumed lack o pay-orperormance at the CEO level, as described by Jensen and Murphy (1990), is more illusory than real taking into account the eect o risk aversion (e.g., Haubrich, 1994). The central message rom these discussions is that, although the pay-perormance sensitivity might be small due to the risk aversion o the agent, it still can provide signiicant incentives. This indicates that risk aversion can have a signiicant eect on the use o perormance measures or incentive purposes. In order to get a better understanding o the use o (accounting) perormance measures in CEO compensation contracts, it is thereore important to empirically examine the eect o risk aversion. Building on the linear principal-agent model o Holmström and Milgrom (1987), this study identiies proxies or managerial risk aversion that can be measured using publicly available executive compensation data. The theoretical analysis indicates that two proxies are worthy o attention, i.e., (1) the variance o compensation and () mean compensation divided by variance o compensation. The irst proxy is based on the assumption that risk averse managers preer less risk to more risk. Thereore, i the principal-agent model is descriptive o observed practices, the variance o compensation should be lower or more risk averse managers. The assumption underlying the second proxy is that risk averse managers demand a risk premium. Thereore, the ratio o the mean compensation to the variance o compensation should be higher or more risk averse managers. We empirically examine the eect o the two risk aversion proxies on the sensitivity o compensation to perormance ater controlling or other economic determinants. The empirical results provide strong support or the principal-agent model predictions. First, consistent with previous research, we ind that the use o accounting perormance measures or incentive purposes decreases with its relative noise and the existence o growth opportunities. The use o market perormance measures also decreases with its relative noise 3

5 but is not aected by growth opportunities. Additional tests indicate that this latter inding can be explained by an increased use o stock-based compensation rather than cash compensation when growth opportunities increase. Second, the empirical results show that the use o both accounting and market perormance measures decreases as the level o risk aversion increases. Further, the impact o risk aversion on the use o accounting perormance measures increases as the relative noise increases and/or the growth opportunities increase. This implies that as accounting perormance measures become less useul due to measure-speciic characteristics, the impact o agent-speciic characteristics, i.e., risk aversion, on the use o these perormance measures increases. Overall, the results suggest that risk aversion plays an important role in the design o executive compensation contracts. The remainder o this paper is organized as ollows. In section 1, we describe the theoretical model that underlies our theoretical and empirical analysis. In section, we develop two risk aversion proxies based on our theoretical model. In section 3, we present the empirical results using the risk aversion proxies and perorm several sensitivity analyses and additional tests. Section 4 concludes this paper with some additional comments and directions or urther research. 1. Theoretical Model To acilitate our analysis, we use a simple linear principal-agent model (Holmström and Milgrom, 1987). The model contains the ollowing assumptions. There is a risk neutral principal who hires a risk and work averse agent to run the irm. The principal is interested in maximizing the gross-payo to the irm x, characterized by x = e + ε (1) where e is managerial eort and ε is the random shock aecting the gross-payo. This grosspayo is assumed to be noncontractible (c. Feltham and Xie, 1994). The agent has a negative 4

6 exponential utility unction over wealth. The eort aversion o the agent is relected by his personal cost o eort, characterized by 1 C ( e) = e () The principal designs a linear incentive contract based on perormance measure y, i.e., s( y) = α + βy (3) where α is a ixed salary and β is the incentive weight. Perormance measure y is characterized by y = e +θ (4) where 0< 1 is the marginal contribution o managerial eort to perormance measure y and θ is the random shock that aects y, with θ ~ N(0,σ²). The principal s problem can be ormulated as ollows max e 1 e r ( β σ ) (5) * s. t. e = β (6) Solving the principal s problem leads to the ollowing incentive weight β = + rσ (7) This equation shows that the incentive weight is a unction o the sensitivity o the perormance measure to managerial eort, the noise o the perormance measure, and the level o managerial risk aversion. Dierentiating the incentive weight with respect to each o the above parameters leads to proposition 1. Proposition 1: dierentiating the incentive weight (β) with respect to the sensitivity o the perormance measure to managerial eort (), perormance measure noise (σ²), and risk aversion (r) leads to 5

7 β > 0 i ² < rσ² β < 0 σ β < 0 r Proposition 1 states that the incentive weight is a decreasing unction o perormance measure noise and managerial risk aversion. Furthermore, the incentive weight is an increasing unction o the sensitivity o the perormance measure to managerial eort i ²<σ². That is, the incentive weight increases with sensitivity i the ollowing assumptions apply: 1. the agent is risk averse to some extent (see e.g., Lambert et al. (1991) or empirical evidence); and. the incentive weight is less than 0.5. That is, the perormance measure is not owned by the agent and most o the output accrues to the principal (see e.g., Jensen and Murphy (1990) or empirical evidence). Under these assumptions, ²<σ² and the incentive weight increases with the degree to which the perormance measure is sensitive to the level o eort.. Risk Aversion Proxies The principal-agent model and the predictions it makes can be used to indicate how empirically observable variables can proxy or the level o risk aversion o the agent. The empirical researcher is able to observe the average level o compensation and the variance o compensation. The ollowing analysis shows how these empirically observable measures can be used to approximate the level o managerial risk aversion. Assume that there exist two types o agents, extremely risk averse (r ) and close to risk neutral (r 0). The extremely risk averse agent has the ollowing incentive weight β = 0 lim r (8) 6

8 That is, the incentive weight is zero, which means that he receives a ixed salary and the variance o compensation is zero. For the close to risk neutral agent, on the other hand, the incentive weight is as ollows β 1 lim r 0 (9) That is, the incentive weight is at least 1, which implies that the variance o compensation at least equals the variance o the perormance measure. As a result, given the predictions o the principal-agent model, we can gain inormation about the risk aversion o agents by empirically observing the variance o compensation. To explain this result more ormally, we calculate comparative static predictions about the eect o risk aversion on the variance o compensation. The variance o compensation is deined by β²σ². Thereore, given the optimal incentive weight, the variance o compensation equals Var[ C] σ + rσ = [ ], (10) which can be rewritten into Var[ C] = ( σ + rσ ) (11) The eect o risk aversion on the variance o compensation can be determined by dierentiating Var[C] with respect to r, which leads to Observation 1. Observation 1: the partial derivative o Var[C] to r is characterized by Var[ C] < 0 r (1) Observation 1 shows that the variance o compensation decreases as the level o risk aversion increases. Further, the linear principal-agent model indicates that the certainty equivalent o the agent (CEA) equals the agent s expected compensation minus the risk premium, i.e., 7

9 r CEA = E[ C] Var[ C] (13) Without loss o generality, we can assume that the agent s reservation utility equals zero, which means that CEA equals zero. As a result, the CEA can be rewritten into E[ C] r = Var[ C] (14) Note, however, that the expected compensation E[C] includes the agent s personal cost o eort, which is empirically unobservable. The only component o E[C] that can be empirically observed is the expected value o the linear incentive contract E[s(y)]. Given the optimal solution to the principal-agent model, the expected value o the incentive contract can be written as (see appendix) E s( y)] = ( + rσ [ ) (15) Thereore, the ratio o E[s(y)] to Var[C] is characterized by E [ s( y)] + = Var[ C] rσ σ (16) Observation : the partial derivative o (E[s(y)] / Var[C]) to r is characterized by ( E[ s( y)]/ Var[ C]) r > 0 (17) Observation indicates that the ratio o E[s(y)] to Var[C] increases as the level o risk aversion increases. In sum, the previous analysis indicates that measures o the variance o compensation and the mean over variance o compensation can be used as proxies or the level o managerial risk aversion. 3. Empirical Analysis In this section, we empirically investigate whether risk aversion has an eect on the compensation-perormance relation, as predicted by the principal-agent model. More 8

10 speciically, Proposition 1 states that the higher the level o risk aversion the lower will be the incentive weight. Applying this to the use o both accounting measures o perormance and market measures o perormance leads to the ollowing hypotheses. Hypothesis 1: The sensitivity o compensation to accounting perormance is negatively aected by the level o managerial risk aversion. Hypothesis : The sensitivity o compensation to market perormance is negatively aected by the level o managerial risk aversion. In testing the above hypotheses, we control or two other economic determinants o the compensation-perormance relationship used in previous research (e.g., Lambert and Larcker, 1987; Baber et al., 1996). More speciically, we control or the impact o sensitivity and noise on the incentive weight. First, we control or the growth opportunities o the irm by using the market-to-book ratio. We expect that the use o accounting (market) perormance measures decreases (increases) with the market-to-book ratio because the relative sensitivity o accounting (market) perormance measures decreases (increases) as the growth opportunities increase (c. Lambert and Larcker, 1987; Baber et al., 1996). Second, we control or the noise in accounting and market perormance measures by adding the variable relative noise o the perormance measures. We expect that the use o perormance measures decreases with its relative noise (c. Lambert and Larcker, 1987). 3.1 Data and Sample Selection We obtain CEO compensation and irm perormance data rom the ExecuComp database or the years CEO compensation data and data on accounting perormance and stock returns or ive consecutive years within the period are available or 955 CEOs. 1 We remove the years in which the executive became CEO or, i the exact date is not available, the irst year or which ExecuComp reports the CEO s compensation data. In order to reduce the inluence o outlier observations, we also remove 9

11 observations with ΔROE 100%. These large changes in Return on Equity are generally caused by low values o stockholders equity due to extreme losses in the previous iscal years. Deletion o partial-year CEOs and observations with ΔROE 100% yields a total sample o 86 CEOs and 3,448 irm-year observations. Panel A o table 1 summarizes the descriptive statistics or the irm-year observations o CEO compensation and irm perormance. The average total cash compensation o the CEOs is $1,38,000, which consists o an average salary o $654,000 and an average bonus o $79,000. The average irm perormance in terms o ΔROE (RET) is -0.3% (19.3%). Panel B o table 1 provides the descriptive statistics with respect to the irm-speciic observations o the risk aversion, noise, and growth opportunities proxies. The two risk aversion proxies have the ollowing deinitions. First, we measure the variance proxy (COMPVAR) by calculating the ive-year variance o total cash compensation. Second, we measure the mean-overvariance proxy (MEANVAR) as the ratio o the ive-year mean o total cash compensation to the ive-year variance o total cash compensation. The mean o COMPVAR (MEANVAR) equals $410 million (0.45). The volatility o accounting perormance (ROEVOL) and market perormance (RETVOL) is measured by the ive-year standard deviation o ΔROE and the ive-year standard deviation o annual stock returns, respectively. The mean o ROEVOL (RETVOL) equals 6.9% (38.%). In conormity with Lambert and Larcker (1987), we measure the relative noise o accounting perormance measures (RELNOISE) by the ratio o ROEVOL to RETVOL, which averages 0.3. Finally, we use the average market-to-book ratio (MTB) over ive consecutive years as a proxy or the irm s growth opportunities. The average MTB equals

12 Insert table 1 about here As can be inerred rom table 1, the empirical distributions o the risk aversion, noise and growth opportunities proxies are skewed. Thereore, we transorm these variables into ranks between 0 and 1. This ranking procedure has several advantages other than eliminating the skewness in the distribution. First, the inormation content o the rank-transormed variables is similar to that o the original variables. Second, because the ranks represent the cumulative distribution unction (CDF) o the variables, we can compute the pay-perormance sensitivity or any point on the distribution o the variables (c. Aggarwal and Samwick 1999), which allows an interpretation o the incentive weights or dierent combinations o the economic determinants. The rank-transormation or both risk aversion proxies is such that a higher rank implies higher risk aversion. Table presents the Pearson correlation coeicients between the economic determinants Insert table about here Speciication o Empirical Model To test the principal-agent model predictions, we examine the ollowing three regression models. Δln(Comp it ) =α 0 + α 1 ΔROE it + α RET it + α 3 RELNOISE i + α 4 MTB i + α 5 (ΔROE it RELNOISE i ) + α 6 (RET it RELNOISE i ) + α 7 (ΔROE it MTB i ) + α 8 (RET it MTB i ) + e it (M1) Δln(Comp it ) =α 0 + α 1 ΔROE it + α RET it + α 3 RELNOISE i + α 4 MTB i + α 5 COMPVAR i 11

13 + α 6 (ΔROE it RELNOISE i ) + α 7 (RET it RELNOISE i ) + α 8 (ΔROE it MTB i ) + α 9 (RET it MTB i ) + + α 10 (ΔROE it COMPVAR i ) + α 11 (RET it COMPVAR i ) + e it (M) Δln(Comp it ) =α 0 + α 1 ΔROE it + α RET it + α 3 RELNOISE i + α 4 MTB i + α 5 MEANVAR i + α 6 (ΔROE it RELNOISE i ) + α 7 (RET it RELNOISE i ) + α 8 (ΔROE it MTB i ) + α 9 (RET it MTB i ) + + α 10 (ΔROE it MEANVAR i ) + α 11 (RET it MEANVAR i ) + e it (M3) where Δln(Comp it ) = year t-1 to year t change in the natural log o CEOs total cash compensation; ΔROE it = year t-1 to year t change in net income beore extraordinary items scaled by common equity; RET it = year t-1 to year t change in stock price plus dividends scaled by year t-1 stock price; RELNOISE i MTB i = ROEVOL scaled by RETVOL (rank-transormed); = the mean ratio o the market value o common equity to the book value o common equity measured over ive consecutive years (ranktransormed); COMPVAR i = the variance o CEO cash compensation measured over ive consecutive years (inverted and then rank-transormed); MEANVAR i = the mean o CEO cash compensation over ive consecutive years scaled by the variance o CEO cash compensation over the same period (rank-transormed). We perorm a pooled cross-sectional analysis over the time period To accept hypotheses 1 and, the regression coeicients α 10 and α 11 in model (M) and model 3 (M3) 1

14 should be signiicantly negative. Negative values or α 10 and α 11 imply that the relationship between compensation and perormance decreases as risk aversion increases. 3.3 Empirical Results Table summarizes the results o the regression analysis or all three models. The results or model 1 (M1) indicate that the relationship between changes in cash compensation and ΔROE decreases with RELNOISE and MTB. This suggests that the use o accounting perormance measures or determining CEO s cash compensation decreases as its relative noise increases and the growth opportunities increase. These results are consistent with previous research (e.g., Lambert and Larcker, 1987) and provide urther empirical evidence o the relevance o these economic determinants. Furthermore, the interaction between RET and RELNOISE is signiicantly positive, while the interaction between RET and MTB is not signiicant. Thereore, the use o stock returns or determining CEO s cash compensation increases as the relative noise in accounting earnings increases but is not aected by growth opportunities. A plausible explanation or this latter inding is that as growth opportunities increase, the use o stock-based compensation increases rather than the use o stock returns in CEO s cash compensation. We examine this possibility in section 3.5. The results or model (M) show that the relationship between changes in cash compensation and both ΔROE and RET decreases as COMPVAR increases, which implies that the use o both accounting perormance measures and market perormance measures decreases as risk aversion increases. The last column o table shows the results o the regression analysis using MEANVAR as a proxy or risk aversion (model 3 (M3)). These results indicate that the relationship between changes in cash compensation and both ΔROE and RET decreases as MEANVAR increases. Similar to COMPVAR, these results suggest that the use o perormance measures decreases as risk aversion increases. Although MEANVAR seems to slightly outperorm COMPVAR, the results suggest that the variance in 13

15 compensation predominately determines the ranking in risk aversion, while the mean o compensation makes some minor adjustments to this ranking. Finally, in both model and 3, the results with respect to the interactions between ΔROE (RET) and RELNOISE and MTB are identical to those in model 1. In sum, the empirical results suggest that the use o both accounting and market perormance measures or determining CEO s cash compensation decreases as the level o managerial risk aversion increases. Thereore, the results provide strong support or hypotheses 1 and. Furthermore, the use o accounting perormance measures decreases with its relative noise and the existence o growth opportunities, while the use o market perormance measures increases as the relative noise in accounting earnings increases Insert table 3 about here Economic Determinants and the Use o Accounting Perormance Measures In order to get a better understanding o how the economic determinants simultaneously aect the use o accounting perormance measures, we compute the incentive weight o ΔROE or dierent combinations o RELNOISE, MTB, and MEANVAR. Using the empirical results o model 3, we compute the dierent incentive weights by illing in three dierent values, i.e., 0, 0.5, and 1, or all three economic determinants. The three dierent values represent respectively the lowest, median, and highest observed values o the economic determinants. This procedure yields 7 coeicients (incentive weights), which are presented in table 4. A number o inerences can be drawn rom table 4. First, the results show that, consistent with agency theory, the incentive weights are highest when both RELNOISE and MTB are low. In these circumstances, accounting perormance measures are highly sensitive and relatively precise and are thereore most useul or incentive purposes. The results suggest 14

16 that, or the median level o risk aversion, a one percentage-point increase in ROE leads to a.3% increase in cash compensation. In contrast, when both RELNOISE and MTB are high, the results indicate that accounting perormance measures are not used or incentive purposes. Second, the characterization o the incentive weight in section 1 (equation 7) implies that the same incentive weight can be ound or dierent combinations o the perormance measure properties and the level o risk aversion. Table 4 indicates that or the median level o RELNOISE, MTB and MEANVAR, the incentive weight is approximately one, which implies that a one percentage-point increase in ROE leads to a 1% increase in cash compensation. Approximately the same incentive weight applies to the situation where RELNOISE is high (low), MTB is low (high), and MEANVAR is low (high). Although these last two situations are each other s opposites with respect to sensitivity, noise, and the level o risk aversion, the use o accounting perormance measures or incentive purposes is identical. These results stress the importance o examining multiple determinants and their interactions. Finally, the relative impact o MEANVAR on the use o accounting perormance measure increases with increases in RELNOISE and/or MTB up to the point where accounting perormance are not used anymore, i.e., when both RELNOISE and MTB are high. This suggests that when accounting perormance measures become less sensitive and/or noisier, the relative impact o risk aversion on the incentive weight increases. For example, when both RELNOISE and MTB are low, the incentive weight or low MEANVAR is 37% higher than the incentive weight or high MEANVAR. In contrast, when RELNOISE is high and MTB is low, the incentive weight or low MEANVAR is almost three times the incentive weight or high MEANVAR. Similarly, at the median RELNOISE and high MTB, the incentive weight or low MEANVAR is almost our times the incentive weight or high MEANVAR. Our theoretical interpretation o this inding is the ollowing. When accounting perormance measures are relatively precise, the role o risk aversion is relatively low since 15

17 the perormance measure imposes ew risks on the manager. However, when the perormance measure becomes noisier, the risk imposed on the manager increases and, as a result, the level o risk aversion determines to what extent the manager can cope with these risks, which aects the incentive weight. With respect to the eect o MTB, our interpretation is the ollowing. When growth opportunities increase, managers need to make riskier investments and more long-term oriented decisions. In general, managers who are risk averse are reluctant to make these investments and decisions. These managers should thereore not be compensated based on accounting perormance measures, since this would make them even more reluctant. Although this eect might also apply to managers who are characterized by low levels o risk aversion, the impact is likely to be much smaller, which makes the use o accounting perormance measures in these circumstances less problematic. On the other hand, when growth opportunities are low, the above tradeo becomes less relevant and thereore the impact o risk aversion decreases Insert table 4 about here Sensitivity Analysis In the previous analyses, we used the variance in cash compensation to determine the level o risk aversion. We interpret the result that a lower variance is related to a lower pay-orperormance as evidence o the prediction that increased risk aversion decreases the incentive weight. However, i substitution eects between dierent components o compensation are present, then a lower variance in cash compensation might not be due to increased risk aversion but due to a substitution o cash compensation by, or example, stock-based compensation. Although the presence o a substitution eect will not aect the empirical results, it will result in a dierent interpretation o the results. 16

18 In order to examine whether there are substitution eects, we correlate the risk aversion proxies with the CEO s stake in the irm (STAKE) and the variance in the value o stock options granted to the CEO (OPTIONS). 3 I the examined companies substitute options or shares or cash compensation, the correlation between the risk aversion proxies and both STAKE and OPTIONS should be signiicantly positive. Table 5 presents the Pearson correlation coeicients between the dierent variables. The results indicate that the correlation between the risk aversion proxies and OPTIONS is signiicantly negative, while the correlation between the proxies and STAKE is not signiicant. This suggests that the dierent components o compensation are not used as substitutes and thereore substitution eects cannot explain our results Insert table 5 about here The results in table 3 urther showed that the interaction between MTB and RET is insigniicant, which implies that, contrary to our expectations, the use o stock returns in determining CEO s cash compensation is not aected by the existence o growth opportunities. This insigniicant interaction might be due to an increased use o stock-based compensation when growth opportunities increase. To examine this possibility, we correlate MTB with STAKE. The results show that the correlation between MTB and STAKE is (p<0.01). This signiicant positive correlation provides some evidence that i growth opportunities increase, there is a stronger link between CEO s compensation and stock perormance through an increased use o stock-based compensation (c. Smith and Watts, 199). 4 Our theoretical model predicts that increased risk aversion decreases the incentive weight, which consequently decreases the variance o compensation. The question arises o 17

19 whether the relationship between the incentive weight and variance o compensation will exist even i the incentive weight is not determined by risk aversion. That is, i our theoretical model is not empirically valid and actors that are not taken into account in our model determine the incentive weight, does the variance o compensation still increase with increases in the incentive weight? I so, then our empirical results could be an artiact based on a deterministic relationship. To test whether our results can be artiicially determined, we use the ollowing procedure. We estimate the ollowing basic compensation-perormance regression Δln(Comp it ) =α 0 + α 1 ΔROE it + α RET it + e it (18) Subsequently, we determine a normal distribution or the incentive weights based on the mean regression coeicients and their standard error. We then randomly assign incentive weights rom this normal distribution to the 86 managers, randomly allocate the 3,448 empirically obtained residuals and calculate 3,448 changes in cash compensation based on actual observations o ΔROE and RET. Taking the actual compensation in the irst o the ive years (that was not included in the regression analysis due to dierencing), we predict or each manager the level o cash compensation in the ollowing our years using the calculated changes in cash compensation. Finally, we calculate the risk aversion proxy COMPVAR based on the predicted compensation data and estimate equation (18) adding two interaction terms, i.e., ΔROE it COMPVAR i and RET it COMPVAR i. In estimating the equation, we use the predicted changes in compensation, actual accounting perormance and stock perormance, and the risk aversion proxy based on predicted compensation. The results based on 500 iterations show that the regression coeicients or the interaction between the risk aversion proxy and respectively ΔROE and RET are not signiicant. These insigniicant interactions lead us to reject the possibility that our empirical results are artiicially determined. 18

20 3.6 Alternative Explanation In the empirical analysis we tested the theoretical prediction that incentive weights increase with decreases in risk aversion. The signiicant interactions that we ind in the empirical analysis are consistent with this explanation. However, an alternative explanation or the signiicant interactions might be that incentive contracts are nonlinear and more convex or less risk averse managers. This increase in convexity with decreases in risk aversion will statistically also lead to signiicant interactions. To test whether increased convexity rather than increased incentive weights can explain our results, we perorm the ollowing test. We split the sample based on deciles o MEANVAR and estimate or each o the ten subsamples the ollowing compensation-perormance relationship using Box-Cox transormation (c. Lambert and Larcker, 1987) B(c t,λ) B(c t-1,λ) = β 0 + β 1 ΔROE t + β RET t + ν t (19) where B(c t,λ) is the Box-Cox transormation o c t, which denotes the level o cash compensation in year t divided by the company-speciic ive-year average o cash compensation, with λ indicating the level o convexity. We apply the ollowing Box-Cox transormation: B(c t,λ) = [c λ t 1] / λ when λ 0 (0) B(c t,λ) = log(c t ) when λ = 0 (1) In the estimation procedure, we let λ vary rom 1.0 to 3.0 with increments o I the convexity o incentive contracts drives our results, the parameter λ should increase with increases in MEANVAR, i.e., risk aversion. Figure 1 graphically shows the dierent λs or the ten subgroups o risk aversion. The results indicate that λ does not gradually increase with increases in risk aversion. Further, or seven out o ten subgroups, the conidence interval includes λ=1, which implies linearity. However, we do ind that the compensation-perormance relationship is convex or the lowest 19

21 two deciles o risk aversion, while it is concave or the highest decile. Although it is unlikely that this inding drives our original results, we re-estimate model and 3 using the data o the seven deciles or which λ=1 is in the conidence interval. The results (not reported) are quantitatively similar to those presented in table 3. Overall, the results suggest that, although we observe non-linearities in the extremes o risk aversion, these non-linearities do not drive our results and we thereore conclude that our empirical indings cannot be explained by changes in the convexity o incentive contracts Insert igure 1 about here Concluding Remarks In this paper, we examine the role o risk aversion in executive compensation contracts. The empirical results provide strong support or the principal-agent model prediction that the use o perormance measures or incentive purposes decreases as risk aversion increases. The results urther show that, consistent with the principal-agent model prediction, measurespeciic characteristics and agent-speciic characteristics simultaneously determine the incentive weight. Finally, the empirical results indicate that the impact o risk aversion on the incentive weight increases as the perormance measure becomes less sensitive and/or noisier. The contribution o this paper is twoold. First, we provide strong evidence o the relevance o incorporating risk aversion in executive compensation research. The results indicate that risk aversion has a signiicant eect on the use o perormance measures, which suggests that uture executive compensation research should thereore take the level o risk aversion into account. Second, the risk aversion proxies that we test are robust, simple, and can easily be measured using publicly available data. As a result, these proxies can be used in uture accounting research other than in the executive compensation area. Areas in which the 0

22 1 risk aversion measures can be applied are, or example, earnings management, CEOs inancing and investment decisions, and voluntary disclosure issues. Appendix: Proos The expected value o the incentive contracts can be determined as ollows. The certainty equivalent o the agent (CEA) is characterized by ) ( 1 σ β β α r e y CEA + = Replacing y by e leads to ) ( 1 σ β β α r e e CEA + = Filling in the optimal eort level, i.e., e * = β, results in ) ( 1 σ β β β α r CEA + = Replacing β by the characterization o the optimal incentive weight, i.e., equation 7, leads to ) ] ([ ] [ 1 ] [ σ σ σ σ α r r r r CEA = By setting the CEA equal to zero, we can solve or α ) ( ) ( σ σ α r r + = Given this characterization o the ixed wage, the expected value o the incentive contract equals ] [ ) ( ) ( )] ( [ r r r y s E σ σ σ =, which can be rewritten into ) ( )] ( [ rσ y s E + =

23 Acknowledgements We grateully acknowledge the comments and suggestions made by Rajesh Aggarwal, Chris Ittner, Rick Lambert, Ken Merchant, and seminar participants at the 3rd annual EAA conerence in Munich, the 001 AAA Management Accounting Research Conerence in Savannah, and the accounting seminar o Maastricht University.

24 Reerences Aggarwal, R.K., and A.A. Samwick. (1999). The Other Side o the Tradeo: The Impact o Risk on Executive Compensation. Journal o Political Economy 107: Baber, W.R., S.N. Janakiraman, and S.H. Kang. (1996). Investment Opportunities and the Structure o Executive Compensation. Journal o Accounting and Economics 1, Baber, W.R., S.H. Kang, and K.R. Kumar. (1999). The Explanatory Power o Earnings Levels vs. Earnings Changes in the Context o Executive Compensation. The Accounting Review 74, Banker, R.D., and S.M. Datar. (1989). Sensitivity, Precision, and Linear Aggregation o Signals or Perormance Evaluation. Journal o Accounting Research 7, Bushman, R.M., and R.J. Indjejikian. (1993). Accounting Income, Stock Price, and Managerial Compensation. Journal o Accounting and Economics 16, 3-3. Feltham, G.A., and J. Xie. (1994). Perormance Measure Congruity and Diversity in Multi- Task Principal/Agent Relations. The Accounting Review 69, Haubrich, J.G. (1994). Risk Aversion, Perormance Pay, and the Principal-Agent Problem. Journal o Political Economy 10, Holmström, B. (1979). Moral Hazard and Observability. Bell Journal o Economics 10, Holmström, B., and P. Milgrom. (1987). Aggregation and Linearity in the Provision o Intertemporal Incentives. Econometrica 55, Jensen, M.C., and K.J. Murphy. (1990). Perormance Pay and Top-Management Incentives. Journal o Political Economy 98,

25 Lambert, R.A., and D.F. Larcker. (1987). An Analysis o the Use o Accounting and Market Measures o Perormance in Executive Compensation Contracts. Journal o Accounting Research Supplement, Lambert, R.A., D.F. Larcker, and R.E. Verrecchia. (1991). Portolio Considerations in Valuing Executive Compensation. Journal o Accounting Research 9, Sloan, R. (1993). Accounting Earnings and Top Executive Compensation. Journal o Accounting and Economics 16, Smith, C.W., and R.L. Watts. (199). The Investment Opportunity Set and Corporate Financing, Dividend, and Compensation Policies. Journal o Financial Economics 3,

26 Table 1. Descriptive statistics Variable Mean Panel A: Firm-year observations (N=3,448) Standard Deviation Median Lower Quartile Upper Quartile Cash salary Cash bonus 79 1, Total compensation 1,38 1,30 1, ,635 ROE RET Panel B: Firm-speciic observations (N=86) COMPVAR (millions) 410, MEANVAR ROEVOL RETVOL RELNOISE MTB Variable deinition: ROE = the change in net income beore extraordinary items scaled by common equity. RET = the annual change in stock price plus dividends scaled by the stock price at the beginning o the year. COMPVAR = the variance in CEO cash compensation measured over ive consecutive years. MEANVAR = the mean o CEO cash compensation over ive consecutive years scaled by the variance o CEO cash compensation over the same period. ROEVOL = the standard deviation o Return on Equity (net income beore extraordinary items scaled by common equity) measured over ive consecutive years. RETVOL = the standard deviation o annual stock returns measured over ive consecutive years. RELNOISE = ROEVOL scaled by RETVOL. MTB = the mean o the market value o common equity scaled by the book value o common equity measured over ive consecutive years. 5

27 Table. Pearson correlation coeicients among rank-transormed variables (p-values are in parentheses). COMPVAR MEANVAR RELNOISE MEANVAR (<0.01) RELNOISE (<0.01) MTB (<0.01) (<0.01) (<0.01) (0.17) Notes: The variables are deined in Table 1. 6

28 Table 3. OLS regression analysis o the eect o risk aversion proxies on the relationship between perormance measures and compensation (White-adjusted t-statistics are in parentheses) Independent variables Risk aversion proxy Model 1 Model Model 3 Basic regression equation COMPVAR MEANVAR Intercept (3.30) *** (.98) *** (3.38) *** ROE.466 (7.0) ***.70 (6.3) ***.608 (6.54) *** RET (1.8) * 0.8 (3.7) *** 0.65 (3.4) *** ROE * RELNOISE (-4.00) *** (-3.69) *** (-3.63) *** RET * RELNOISE 0.18 (.7) ** (.04) ** (.03) ** ROE * MTB (-4.07) *** (-4.7) *** (-3.90) *** RET * MTB (-1.08) (-1.63) (-1.43) ROE * Risk aversion (-.40) ** (-.53) ** RET * Risk aversion (-1.84) ** (-1.85) ** F-value *** *** *** Adjusted R (Continued on next page) 7

29 (Table 3 continued) Notes: ***, **, * is statistically signiicant at respectively the 1%, 5%, and 10% level (two-tailed). Coeicients on the risk aversion proxies, RELNOISE and MTB are included in the regression but not separately reported. The independent variables (except ROE and RET) are rank-transormed variables. 8

30 Table 4. The use o accounting perormance measures or dierent combinations o RELNOISE, MTB, and MEANVAR. RELNOISE MTB Low Median High Low Low MEANVAR Median MEANVAR High MEANVAR Median Low MEANVAR Median MEANVAR High MEANVAR High Low MEANVAR Median MEANVAR High MEANVAR Notes: The variables are deined in Table 1. 9

31 Table 5. Pearson correlation coeicients among rank-transormed variables (p-values are in parentheses). COMPVAR MEANVAR OPTIONS OPTIONS (<0.01) STAKE (0.15) (<0.01) (0.31) 0.45 (<0.01) Notes: OPTIONS = the ive-year variance in the value o stock options granted to the CEO. Options are valued using the Black & Scholes method (as reported by ExecuComp). STAKE = the ive-year mean o the end-o-the-year market value o the company s common shares owned by the CEO plus the end-o-the-year value o exercisable and non-exercisable in-the-money options scaled by the CEO s annual cash compensation. The remaining variables are deined in Table 1. The reported variables are rank-transormed variables. 30

32 3 λ λ HIGH λ * λ LOW Figure 1. The optimal level o λ and conidence intervals or deciles o risk aversion. Lower values o λ imply greater convexity and λ=1 implies linearity. Decile 1 (10) is the lowest (highest) risk aversion group. λ *, λ HIGH, and λ LOW denote the optimal level o λ, the upper 95 percent conidence limit, and the lower 95 percent conidence limit, respectively. 31

33 Endnotes 1 I more than ive years o data are available, we use the data or the last ive years. The results are identical when COMPVAR is used. 3 STAKE is measured as the ive-year mean o the end-o-the-year market value o the company s common shares owned by the CEO plus the end-o-the-year value o exercisable and non-exercisable in-the-money options scaled by the CEO s annual cash compensation. OPTIONS is measured as the ive-year variance in the value o stock options granted to the CEO, where the options are valued using the Black & Scholes method (as reported by ExecuComp). Both STAKE and OPTIONS are rank-transormed. 4 Note that this result does not indicate a substitution eect between dierent components o compensation. Since the use o stock returns in determining CEO s cash compensation is not aected by MTB, it can be concluded that CEOs receive additional incentives when growth opportunities increase. As a result, the use o stock-based compensation is complementary to the use o cash compensation. 3