No Asymmetry in Pay for Luck

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1 No Asymmetry in Pay for Luck Naveen D. Daniel a Yuanzhi Li b Lalitha Naveen c October 2012 Abstract In contrast with current literature, we find no asymmetry in CEO pay for luck. The current literature documents that CEOs are rewarded for performance increases due to good luck but are not penalized to the same extent for performance decreases due to bad luck. These studies are based on either the level of annual pay or the change in annual pay. These measures, however, constitute only a trivial fraction of CEO compensation linked to firm performance (Aggarwal and Samwick (1999)). CEOs are affected by changes in their total firm-related wealth, which in turn is affected to a greater extent by equity holdings rather than annual pay (Jensen and Murphy (1990) and Core and Guay (2002)). We find that, on average, the CEO s firm-related wealth increases by $37 for a $1000 increase in shareholder wealth due to good luck, which is identical to the decrease of $37 for a $1000 decrease in shareholder wealth due to bad luck. JEL Classifications: G32; G34 Keywords: Asymmetry in pay for luck, Pay for luck, Pay-performance-sensitivity, Compensation, Firm-related wealth a LeBow College of Business, Drexel University, Philadelphia, PA, 19104, USA; nav@drexel.edu b Fox School of Business, Temple University, Philadelphia, PA, 19122, USA; yuanzhi.li@temple.edu c Fox School of Business, Temple University, Philadelphia, PA, 19122, USA; lnaveen@temple.edu The authors are grateful for helpful comments from Rajesh Aggarwal, Jay Cai, Eli Fich, Gerald Garvey, Radhakrishnan Gopalan, Swaminathan Kalpathy, Xi Li, Connie Mao, Todd Milbourn, Oleg Rytchkov, Fenghua Song, Ralph Walkling, David Yermack, and seminar participants at Drexel University, Temple University, and Villanova University.

2 No Asymmetry in Pay for Luck Recent studies (Garvey and Milbourn (2006) and Gopalan, Milbourn, and Song (2010)) document an asymmetry in CEO pay for luck. Specifically, these studies show that CEOs are rewarded for firm performance that is attributed to good luck, but not penalized to the same extent for performance that is attributed to bad luck. The findings of Garvey and Milbourn (2006) have been interpreted by several studies as being consistent with the rent extraction view of compensation contracts. 1 Using an improved research design that is grounded in prior literature, we find no asymmetry in pay for luck. Previous studies that examine asymmetry in CEO pay for luck estimate regressions where the dependent variable is change in annual pay (Garvey and Milbourn (2006)) or the level of annual pay (Gopalan, Milbourn, and Song (2010)), and the independent variables are measures of dollar stock returns attributable to good luck and bad luck. 2 In contrast, our dependent variable is the annual change in the CEO s firm-related wealth, which includes the annual pay but also the value change from the CEO s stock and option holdings. The change in firm-related wealth is affected to a greater extent by equity holdings rather than annual pay. In fact, Aggarwal and Samwick (1999) find that the pay-performance-sensitivity estimated using the change in the CEO s firm-related wealth is about 20 times higher than that estimated using the change in annual pay and 33 times higher than that estimated using the level of annual pay. 3 Thus, Garvey and Milbourn (2006) and Gopalan, Milbourn, and Song (2010), by focusing on 1 For example, Frydman and Jenter (2010, pg. 16), in their survey of the compensation literature, state Rent extraction is also suggested by the observation that CEOs are frequently rewarded for lucky events that are not under their control (such as an improving economy) but not equally penalized for unlucky events (Bertrand & Mullainathan 2001, Garvey & Milbourn 2006). 2 Gopalan et al. use the term pay for sector performance rather than pay for luck. 3 The numbers are based on the pay-performance-sensitivity for the median-risk firm reported in Model 1, Panel A of Table 3 (pay-performance-sensitivity = ), Model 1, Panel A of Table 4 (pay-performance-sensitivity = 0.732)), and Model 2, Panel A of Table 4 (pay-performance-sensitivity = 0.432) of their paper. 1

3 annual pay, are effectively examining only a small slice of the overall pay-for-performance sensitivity. The conclusions from such studies, therefore, may be premature. Two related strands of the literature provide strong support for our choice of change in the CEO s firm-related wealth as the dependent variable. First, early papers that examine ex-post pay-for-performance but without separating performance into skill and luck use the annual change in the CEO s firm-related wealth (Jensen and Murphy (1990), Hall and Liebman (1998), Aggarwal and Samwick (1999), and Milbourn (2003)). These studies use the term payperformance-sensitivity (PPS) a misnomer in some sense to represent the change in CEO firm-related wealth associated with the change in shareholder wealth. Hall and Liebman (pg. 670) argue that CEOs care about changes in their wealth emanating from all sources, not just salary and bonus and that changes in firm-related wealth that include changes in the value of stocks and options...is the right measure of monetary incentives. The idea that change in wealth is more important to managers is reinforced by the loss in firm-related wealth, suffered by the CEOs of firms such as Bear Sterns and Lehman Brothers, resulting from the steep fall in their share prices. As Yermack (2009b) notes, CEOs of financial firms received several million dollars in salary and perks, but their wealth declined significantly in 2008 as their stock prices nosedived. He argues that this indicates a robust pay-for-performance system. Fahlenbrach and Stulz (2011) provide validation for Yermack s arguments by showing that bank CEOs suffered large wealth losses during the recent crisis. Second, the ex-ante managerial incentives literature (Guay (1999) and Core and Guay (1999, 2002)) considers incentives from the entire portfolio of stock and options, and not just those from annual grants. Indeed, Core and Guay (2002) argue that [f]ailure to capture all the components of CEOs equity incentives results in measurement error that can either reduce the 2

4 power of the researcher's tests or lead to spurious inferences. We capitalize on improved data availability and refine the methodology used in earlier studies (Jensen and Murphy (1990), Hall and Liebman (1998), and Aggarwal and Samwick (1999)) to more precisely estimate the change in the CEO s firm-related wealth. These studies have estimated changes in firm-related wealth typically by multiplying the starting portfolio of stock and options by their corresponding return during the year and then adding the annual pay (which includes the value of equity grants). This method assumes that CEOs do not engage in stock sales, stock purchases, or option exercises during the year, and also ignores option repricing, options expiring out of the money, and any change in value of equity grants from the grant date to the fiscal year end date. Our methodology addresses these limitations. Section II.A and the Appendix provide more details of our measure of changes in firm-related wealth. We use data from ExecuComp for the period to be comparable with Gopalan, Milbourn, and Song (2010) and to help us isolate the impact of changing the dependent variable on pay-for-luck asymmetry. 4 Our results are robust to extending the sample period to We find that the average value of the stock and option portfolio ($61.90M) is many times larger than the average annual pay ($3.83M). Thus it is reasonable to believe that wealth gain is driven primarily by changes in value of the stock and option portfolio and not by the change in annual pay or the level of annual pay. Consistent with this, we find that the average change in firm-related wealth ($11.31M) is significantly larger than the average change in pay ($0.21M). Our estimate of annual changes in the CEO s firm-related wealth has a correlation of 0.16 with the change in annual pay and a correlation of 0.23 with the level of annual pay. The low 4 Garvey and Milbourn include data from while Gopalan et al. include data from We do not include 2006 because this was the transition year when firms changed their compensation reporting significantly as part of FAS 123R requirements. In 2006, about 15% of firms still reported their data using the old reporting format. We wish to ensure that our results are not driven by changes in these reporting requirements. Our results are unaffected if we include 2006 in our sample. 3

5 correlations suggest that examining change in wealth need not lead to the same inferences as examining change in pay or level of pay. We start by replicating the key specifications in the papers that document pay-for-luck asymmetry: Model 1, Table 5 of Garvey and Milbourn (2006, henceforth GM) and Panel A, Table 9 of Gopalan, Milbourn, and Song (2010, henceforth GMS). Similar to these studies, we find asymmetry in pay for luck. We then replicate the same regressions, but using our estimate of annual change in the CEO s firm-related wealth as the dependent variable. We now find no asymmetry in pay for luck. We find that the CEO s firm-related wealth increases by $ for a $1000 increase in shareholder wealth due to good luck, which is economically and statistically indistinguishable from the decrease of $ for a $1000 decrease in shareholder wealth due to bad luck. Our evidence does not support the skimming view prevalent in the literature. GM and GMS document pay-for-luck asymmetry in specific subsamples of firms such as those with weak shareholder rights, diversified firms, firms with greater strategic flexibility, and firms with talented CEOs. In contrast to both studies, we find no asymmetry in pay for luck in similar subsamples when we use change in firm-related wealth as the dependent variable. Our results are intuitive: the CEO s firm-related wealth comprises primarily of stock and option holdings, the value of which moves with the stock price. The stock price, in turn, responds in the same manner to both good and bad luck, leading to our finding of no asymmetry. So what explains the GM and GMS results? One possible explanation for the asymmetry in pay for luck documented by GMS is that, in reality, there is a lower bound on annual pay (much higher than zero), which is dictated by the reservation wage demanded by the CEO. Therefore the board, when faced with poor firm performance, cannot reduce CEO pay as much as it would like. This also explains the GM finding of asymmetry in pay for luck, because the change in 4

6 annual pay cannot be significantly negative despite poor performance. We perform several robustness checks to confirm our result. First, we recognize that the widely-used Core and Guay methodology, which we use to compute option values prior to 2006, has some limitations. We rule out the possibility that this methodology biases our results by documenting that our findings continue to hold for the period (where this methodology is not required). Second, we find no evidence of pay for luck asymmetry when we use alternative measures of luck and skill, alternative definitions of change in wealth, alternative non-linear functional forms, different proxies for CEO power, alternative measures of governance, as well as alternative econometric specifications. Third, we examine more closely the link between option compensation and asymmetry in pay for luck. CEO compensation typically includes options, whose values have a convex relation with stock price. Therefore, one might expect a non-linear relation in pay for performance. Moreover, this asymmetry in pay for performance will be stronger if the options are near the money and if the options have shorter time-to-maturity. This asymmetry in pay for performance will not translate into an asymmetry in pay for luck, however, if (i) luck is not highly correlated with overall performance or (ii) annual pay following poor performance is high enough to compensate for the loss in value of equity holdings. While we find a modestly high correlation between luck and performance (=0.53), it is likely that firms give higher equity awards (and hence higher pay) following poor performance to bring the level of incentives closer to target (Core and Guay (1999)). Thus, we do not expect to find a link between the structure of option compensation and asymmetry in pay for luck. Consistent with this, we find no asymmetry in pay for luck even in firms whose CEOs have a significant amount of options (option value accounts for more than 80% of firm-related wealth), whose CEOs have option 5

7 portfolios with a short maturity, or whose CEOs have option portfolios that are near the money. One potential concern here is that our specifications somehow lack the statistical power necessary to reject the implied null of no asymmetry. We believe this is not a valid argument because we are able to replicate the findings in GM and GMS when we use the same dependent variables as in their study. We fail to find their result only when we use change in firm-related wealth as the dependent variable. Moreover, using change in firm-related wealth, we are able to replicate the results in Aggarwal and Samwick (1999). Thus it is unlikely to be a lack of statistical power that is driving our results. Importantly, the results are never economically significant. For our overall sample, change in wealth associated with good luck is almost identical to the change in wealth associated with bad luck. The main contribution of our study is to document that when an all-inclusive measure of incentives changes in the CEO s firm-related wealth is used, there is no asymmetry in pay for luck. Our secondary contribution is methodological: we provide researchers with a methodology to more precisely estimate the changes in the CEO s firm-related wealth. The rest of the paper is arranged as follows. Section I briefly reviews the related literature and establishes the basis for our research design. Section II describes the data and provides descriptive statistics. Section III presents our main results. Section IV presents several robustness tests, and Section V concludes. I. Motivation and Related Literature One of the key predictions of agency theory is that compensation will be designed to incentivize managers to maximize shareholder wealth. One such mechanism is the sensitivity of managerial pay to firm performance. Jensen and Murphy (1990) was the first comprehensive study on pay-performance incentives. The authors estimate that for every $1000 change in 6

8 shareholder wealth, the CEO s firm-related wealth changes, on average, by $3.25, where change in CEO firm-related wealth is calculated as the sum of changes in value of outstanding stock options and stock holdings, annual pay, present value of future changes in salary and bonus, and present value of loss in pay associated with performance-related dismissals. Subsequently, Hall and Liebman (1998) document that the pay-performance sensitivities are much higher than that estimated by Jensen and Murphy, primarily because of the increase in stock option awards over their sample period. They estimate changes in wealth as the increase in the value of the CEO s beginning-of-year holdings of firm stock and options plus salary and bonus plus value of stock and option grants. Aggarwal and Samwick (1999) document that changes in firm-related wealth (calculated similar to Hall and Liebman) are positively associated with firm performance, but this pay-performance sensitivity is a declining function of firm risk. A related strand of literature on relative performance evaluation considers the sensitivity of pay changes to the performance of the firm net of industry (or market) performance (Gibbons and Murphy (1990), Himmelberg and Hubbard (2000), Garvey and Milbourn (2003), Rajgopal, Shevlin, and Zamora (2006)). With the exception of Gibbons and Murphy, all these papers consider changes in firm-related wealth. Bertrand and Mullainathan (2001), although they belong to this broad stream of literature, use the term luck to describe the performance of the firm that can be attributed to external forces (such as oil prices for oil industry firms, or exchange rate movements, or industry returns), and the term skill to describe firm performance net of luck. They find that CEO pay is as sensitive to luck as it is to changes in aggregate firm performance, and the sensitivity of CEO pay to luck is higher in poorly governed firms. They interpret this as evidence of managerial skimming. While the authors note (pg. 905) that [i]deally, the compensation in a given year would also include changes in the value of 7

9 unexercised options granted in previous years [Hall and Liebman, 1998] they use change in pay as the dependent variable because calculation [of wealth changes] requires data on the accumulated stock of options held by the CEO each year, whereas existing data sets including ours, contain only information on new options granted each year. Garvey and Milbourn (2006, GM) contend that higher sensitivity of CEO pay to luck in weakly governed firms is not sufficient to prove rent extraction; rather there should be asymmetry in pay for luck. Specifically, they argue that CEOs would like to be rewarded for good luck, but insulated somewhat from bad luck. Using change in annual CEO pay, they find an asymmetry in CEO pay for luck. This asymmetry is stronger in weakly governed firms. They interpret the overall findings as indicative of rent extraction. 5 Following Bertrand and Mullainathan (2001), GM use change in annual pay rather than changes in firm-related wealth. As mentioned earlier, however, Bertrand and Mullainathan note that pay-for-luck tests should ideally be done using changes in the firm-related wealth of the CEO, but are unable to do so due to data limitations. GM, however, do not suffer from the same data limitations because they use ExecuComp data, which could be used to estimate changes in firm-related wealth. They explain their use of change in pay (rather than change in firm-related wealth) as follows: we ignore changes in the value of CEO s existing shares and options because by definition they move only with the stock price and cannot have distinct sensitivities to luck and skill. While their statement is true, it does not mean that value changes from stock and options holdings can be ignored given the prior literature on pay-for-performance, which documents that CEO s wealth is affected more by equity holdings than by pay. Gopalan, Milbourn, and Song (2010, GMS) use the term pay for sector performance 5 Bizjak, Lemmon, and Naveen (2008, pg. 153) also use change in the CEO s annual pay as the dependent variable, but conclude that asymmetry in pay for luck is more consistent with the use of benchmarking by firms to gauge the [CEO s] market reservation wages. 8

10 rather than pay for luck. They develop a model where pay for luck and asymmetry in pay for luck can both be part of the optimal compensation contract. Consistent with the predictions of their model, they find asymmetry in pay for luck in specific sub-samples of firms such as diversified firms, firms with higher strategic flexibility, and firms with talented CEOs. GMS follow GM, but use the level of annual pay, rather than change in pay, as the dependent variable. It is correct to look at level of pay and relate it to skill and luck only if the entire pay comes in the form of cash awards, or if the equity awards have no vesting provisions in which case the awards can be converted into cash by the CEO. CEOs, however, are paid with stocks and options with vesting provisions, the explicit purpose of which is to incentivize the CEO by providing pay for performance sensitivity. Indeed, Hall and Liebman (1998, pg. 670) comment that...increasing the responsiveness of pay to performance is perhaps the main reason why boards gives CEOs stock and options, both of which typically have restrictions that force the CEOs to hold the stock and stock options. Our work deviates from the pay for luck literature in that we follow early compensation studies (Jensen and Murphy (1990), Hall and Liebman (1998), and Aggarwal and Samwick (1999)) and examine how the CEO s firm-related wealth changes with performance changes due to luck. The CEO s firm-related wealth comprises primarily of stock and options, the value of which moves with the market price of the stock. The market price of stock, in turn, is affected by both good luck and bad luck. It is likely, therefore, that the asymmetry in CEO pay for luck will be weaker or even non-existent when the change in firm-related wealth is considered. II. Data and Summary Statistics We start with individuals identified as CEOs (CEOANN variable) in the Standard & Poor s ExecuComp database for the period We restrict our main tests to the period 9

11 to show that the difference in results between the GM/GMS studies and ours is because of difference in the dependent variable and not due to difference in the sample period. ExecuComp indicates the dates when the CEO assumed office and when the CEO left office, but, in some cases, fails to identify an executive as the CEO even though he or she appears to be the CEO based on these dates. We classify these individuals also as CEOs. As in GM, we restrict our analysis to CEOs with two consecutive years of coverage. A. Calculation of Change in Firm-Related Wealth We estimate the change in the CEO s firm-related wealth as the annual non-equity pay plus the change in value from the equity components (holdings and grants). Non-equity pay is the total compensation (TDC1 variable in ExecuComp) minus the value of shares and options granted during the year. 6 To estimate the change in value from the equity components, we start by computing (i) the change in value of the stock portfolio, which is the value of the stock holdings at the end of the year minus the value of the stock holdings at the beginning of the year, and (ii) the change in value of the option portfolio, which is the value of the option holdings at the end of the year minus the value of the option holdings at the beginning of the year. The value of the stock holdings is the number of shares held by the CEO multiplied by the corresponding stock price. The value of option holdings is estimated using the methodology of Core and Guay (2002), which has been used in numerous papers such as Rajgopal and Shevlin (2002), Coles, Daniel, and Naveen (2006) among others. We first sum up (i) and (ii). This summation already includes the impact of option repricing, option expiry, value of equity grants as of grant date, and the change in value of equity grants from the grant date to fiscal year end date. 6 Harford and Li (2007) use a similar method to study wealth changes of CEOs around acquisition events. 10

12 If the CEO does not sell stock, purchase stock, or exercise options, then the change in value from the equity components is just this summation. Failure to include the CEO s stock sales will result in our initial estimate [= (i) + (ii)] underestimating the true change in the CEO s firm-related wealth because the shares sold are no longer part of the CEO s portfolio at the end of the year. Similarly, failure to include stock purchases will result in our initial estimate overestimating the true change in the CEO s firm-related wealth because the stock portfolio at the end of the year includes stock purchased during the year but the cost of purchasing these shares is not included in the value of the share portfolio at the beginning of the year. Finally, failure to include the cost of option exercise (exercise price number of options exercised) will result in our initial estimate overestimating the true change in the CEO s firm-related wealth because the shares obtained from exercise are considered as part of the stock portfolio at the end of the year, but the cost incurred by the executive in exercising the options has not been taken into account. We use insider trading data from Thomson Reuters to estimate the value of shares sold, the value of shares purchased, and the cost of options exercised. 7 For each CEO, for each year, we estimate the change in firm-related wealth as the change in value of the stock portfolio, plus change in value of the option portfolio, plus dollars realized from stock sales by the CEO, minus dollars paid for stock purchases by the CEO, minus dollars paid to exercise options by the CEO, plus the non-equity pay. We provide more details as well as an example in the Appendix, and also discuss how our methodology compares with that used by existing studies. Section IV.D documents that our results are similar when we use wealth 7 CEOs often donate their shares in the firm to charitable organizations (Yermack (2009a)). We consider such donations also as stock sales because if the CEO did not denote the sale as a gift, but instead sold stock and donated the cash proceeds to charity (something which we would not observe), then we would have considered the stock sales in our estimate of firm-related wealth. The intent of usage of the funds realized from stock sale should not impact our estimate of firm-related wealth. Hence we do not distinguish between stock sales and stock donations. For the same reason, we do not consider the tax break that the CEO receives from the stock donation. 11

13 changes computed as in Jensen and Murphy (1990), Hall and Liebman (1998), and Aggarwal and Samwick (1999). Our results are also similar if we exclude the potential gains that the CEO could make from informed trading (through sales, purchase, and option exercise). B. Estimation of Luck and Skill To identify changes in firm value due to luck and skill, we follow GM and GMS and regress the firm s annual stock returns on the equal-weighted and value-weighted industry returns (based on two-digit SIC), and time dummies. As in their papers, we (i) do not include the firm s returns in the industry returns, (ii) do not include an intercept term, and (iii) eliminate all firms that do not have a December fiscal-year end to ensure that the performance measures for all firms are over the same time period. 8 As in GM and GMS, Luck is the predicted value from the regression multiplied by the firm s market capitalization at the beginning of the year. Skill is the residual stock returns multiplied by the firm s market capitalization at the beginning of the year. Thus Luck and Skill are measured in dollar values rather than rates of return. 9 C. Descriptive Statistics Panel A of Table I reports summary statistics for the key variables used in our study. To avoid any large outliers influencing the results, we winsorize all variables at their 1 st and 99 th percentiles. We find similar results using median regressions (Section IV.I). The firms in our sample are large, with mean sales of $3,797M. This is not surprising as 8 We find our results are robust to alternative definitions of luck and skill (Section IV.C) as well as to the inclusion of firms with non-december fiscal-year ends (Section IV.H). 9 One issue with studies that use ExecuComp data (including our study, GM, and GMS) is that firms could exit the sample either because they get taken over (in which case they have high returns in the final year) or get delisted (in which case they have poor returns in the final year). In both cases, ExecuComp does not report data on the firm in the year of exit. This, however, is less of a concern in our study because any firm-specific performance that leads to very good or very bad returns will be attributed (by the regression) to skill, not luck. This is because skill is defined as the residual from a regression of stock returns on industry returns. This data limitation should, therefore, affect the pay for skill relation and not the pay for luck relation. 12

14 the sample comprises the S&P 1500 firms. The average value of the stock and option portfolio ($61.90M) is many times larger than the average annual pay ($3.83M). Likewise, the average change in firm-related wealth ($11.31M) is significantly larger than the average change in annual pay ($0.21M). Thus it is very reasonable to conclude that wealth change is driven primarily by change in value of the stock and option portfolio and not by level of pay or change in pay. The mean values of Luck and Skill are $977M and $398M. In comparison, GM report values of $946M and $160M. Our median values of Luck and Skill are $136M and $30M. GM report medians of $155M and $36M respectively. In Panel B, we report correlations between our key variables. Change in firm-related wealth (our main variable) has a correlation of 0.16 with change in pay (main variable used in GM) and 0.23 with the level of pay (main variable used in GMS). The low correlations suggest that examining change in wealth need not lead to the same inferences regarding asymmetry in pay for luck as examining change in pay or level of pay. Change in pay and level of pay have a relatively high correlation (=0.43), which might explain why GM and GMS find similar results on pay for luck even though they use different dependent variables. III. Main Results In this section, we present our main results relating to asymmetry in pay for luck. A. Is There Asymmetry in Pay for Luck? Since we follow the early literature on PPS by using change in firm-related wealth (Jensen and Murphy (1990), Hall and Liebman (1998), and Aggarwal and Samwick (1999)), we first benchmark our results against some of these studies. We consider the specification in Table III, Panel A, Column 1 of Aggarwal and Samwick (1999), who also use data from ExecuComp. The results are reported below, with t-statistics in parentheses. 13

15 ΔWealth = Dollar Returns Dollar Returns Cdf Variance of Dollar Returns (155.92) ( ) Cdf Variance of Dollar Returns [N=10,199, pseudo R 2 =0.11] (18.43) Dollar Returns is given by the fiscal year stock return multiplied by the beginning-ofyear market capitalization. Cdf Variance of Dollar Returns is the cumulative distribution function (CDF) of the variance of dollar returns in the sample and ranges from zero to one. As in Aggarwal and Samwick, the variance of dollar returns is computed as the variance of monthly stock returns over prior five-year windows multiplied by the market capitalization at the beginning of the year. The results (positive coefficient on Dollar Returns and negative coefficient on the interaction term) are consistent with Aggarwal and Samwick. In terms of economic significance, for a firm of median risk (cdf = 0.5), the change in the CEO s firmrelated wealth for a $1000 change in shareholder wealth is $18.04 (= ), which is 24% higher compared to Aggarwal and Samwick s estimate of $ Having established the similarity of our results with the prior literature on payperformance-sensitivity, we then replicate prior studies that have documented an asymmetry in the sensitivity of pay for luck. Table II presents the results. Here and in the rest of the paper, we include year and executive fixed effects, and the p-values are based on robust standard errors as in GM. In our robustness section (Section IV.J), we show that all our results hold when we include firm fixed effects or industry fixed effects instead of executive fixed effects, as well as when standard errors are clustered at the firm level (Petersen (2009)). In Model 1, we replicate Column 1 of Table 5 of GM. Bad Luck and Bad Skill are 10 The specification above is based on median regressions using unwinsorized data, to be consistent with Aggarwal and Samwick. Aggarwal and Samwick also do OLS estimation in Table 5 of their paper. Our PPS estimate (again using unwinsorized data) from OLS regressions is $79 change in CEO firm-related wealth for every $1000 change in shareholder wealth. This is comparable to theirs (=$69). 14

16 indicator variables that equal one when Luck and Skill are negative, and zero otherwise. Cdf Variance of Luck and cdf Variance of Skill are CDF of variance of Luck and Skill respectively. 11 We find evidence of asymmetry in pay of luck, consistent with GM. The coefficient on Luck is significantly positive, while the coefficient on Luck interacted with Bad Luck, which is our key variable of interest, is significantly negative. This indicates that executives are rewarded for good luck, but not punished as much for bad luck. The economic magnitude of this effect is also similar to GM when luck is up, the pay for the CEO of a median-risk firm increases by 70 cents (= ), but when luck is down, it decreases only by 51 cents (= ). The corresponding numbers in GM are 79 cents and 60 cents. 12 In Model 2, we replicate the asymmetric pay for luck results documented in Panel A, Table 9, of GMS using the level of annual pay as the dependent variable. As in GMS, we find asymmetry in pay for luck: the coefficient on Luck Bad Luck is significantly negative. 13 Model 3 is our key specification. The dependent variable is the change in the CEO s firm-related wealth. The positive coefficient on Luck indicates there is pay for luck. However, the coefficient on the interaction term of Luck and Bad Luck is now insignificant. This suggests that the change in the CEO s firm-related wealth is equally sensitive to good luck and bad luck. 11 It is not clear how Variance of Luck and Variance of Skill are computed in GM and GMS. We therefore compute these variances using the same method that we use to compute Variance of Dollar Returns; that is, we use five year rolling windows. Our estimates of variances, however, are based on annual data because our estimates of luck and skill (based on the GM and GMS approach) are only available at the annual level. Our results are similar if we use the entire sample period to compute the variances of luck and skill instead of five-year windows, and use this single point estimate for each firm for all the years the firm is in the sample. 12 We get similar results when we restrict the sample to CEOs that have tenure greater than two years. This ensures that we do not consider pay changes of CEOs who received compensation only for part of the current or prior year. 13 GMS, even though they follow GM, do not include the interaction term of Skill and Bad Skill in their Table 9 regressions where they examine asymmetry. This is possibly because GM include this interaction only in their initial specifications when they do subsample analysis, they drop this variable. To be consistent with our earlier specification which is based on GM (Model 1), we include this interaction term in Model 2. The results in Table II are similar if we exclude this variable. 15

17 We conclude that there is no asymmetry in pay for luck when the CEO s firm-related wealth is considered. 14 In economic terms also, the asymmetry is insignificant. The results show that for a firm of median risk, the CEO s firm-related wealth increases by $37.21 (= ) for every $1000 increase in shareholder wealth due to good luck and decreases by the same amount, $37.21 (= ), for every $1000 decrease in shareholder wealth due to bad luck. B. Is Asymmetry in Pay for Luck Reflective of Skimming? GM argue that if asymmetric pay for luck is symptomatic of skimming, then such asymmetry should be greater in firms with weak governance. They find evidence consistent with this skimming hypothesis. As in GM, we classify firms as weakly governed if the Gompers, Ishii, and Metrick (2003) index is greater than or equal to 12. Row 1 of Table III reports the regression results based on Model 3 of Table II for the subsample of firms with weak governance. For simplicity we present only the coefficients on Luck, Luck Bad Luck, and Luck cdf Variance of Luck (this last term is presented so that the economic significance of pay for luck can be estimated). The coefficient on the Luck Bad Luck variable remains insignificant implying that there is no asymmetry in pay for luck even in weakly governed firms. C. Is there Asymmetry in Pay for Luck Consistent with the Model of GMS? GMS argue that asymmetric pay for luck could be optimal when the firm s exposure to sector performance is endogenous and at the discretion of the CEO. They show, both theoretically and empirically, that diversified firms, firms with strategic flexibility, and firms with talented CEOs exhibit asymmetry in pay for luck. We therefore examine whether asymmetric pay for luck exists for the specific subsamples of firms hypothesized in GMS, when 14 GM find that the coefficient on Luck Bad Luck is significantly different from the coefficient on Skill Bad Skill. They argue that such a finding is inconsistent with optimal contracting. Since GMS do not have this interaction term, they do not do this test. We find that the coefficients are only weakly different from each other (p = 0.103) in Model 1 and not significantly different from each other in Models 2 and 3. 16

18 we use the change in the CEO firm-related wealth as the dependent variable. The definitions of the subsamples follow GMS. Diversified firms are those that operate in more than one business segment. As in GMS, firms in industries whose median market-to-book ratio is above the 60 th percentile of the overall market-to-book ratio, and firms in industries whose median R&D-toassets ratio is above the 70 th percentile of overall R&D-to-assets ratio are considered as having greater strategic flexibility. Talented CEOs are those whose firms have above-median industryadjusted returns or CEOs who are outsiders at the time of becoming the CEO. 15 Rows 2 6 of Table III report the results for different subsamples based on Model 3 of Table II. In all cases, the coefficient on Luck Bad Luck remains economically and statistically insignificant, indicating that, once change in CEO wealth is used rather than the level of CEO pay, there is no asymmetry in pay for luck in any of the sub-samples considered by GMS. IV. Robustness In this section, we perform several robustness tests, using our key specification (Model 3 of Table II). Results are reported in Table IV. We focus on the coefficient on Luck Bad Luck. A significantly negative coefficient implies asymmetry in pay for luck. As before, we also report the coefficients on Luck and Luck cdf Variance of Luck so that the economic significance of the asymmetry in pay for luck can be assessed. A. Is the Core and Guay Methodology Driving Our Results? Prior to 2006, firms had to report details only for newly granted options. For previously granted unvested and vested options, only the aggregate intrinsic value of each portfolio had to be reported. The widely-used Core and Guay (2002) methodology that we follow makes some 15 For the subsample of outsider CEOs, GMS classify firms into two groups based on whether the CEO s four factor Carhart alpha at his or her previous firm was positive or negative. We do not have information on where the external CEO came from, so we do not consider this proxy for CEO talent. 17

19 assumptions to estimate the value of the option portfolio, which could potentially lead to the change-in-wealth measure being estimated less precisely. We consider here whether this limitation, which is discussed in depth in Core and Guay, biases our results. First, we take advantage of the fact that, as part of the changes mandated by FAS123R, firms disclose tranche level data on all options outstanding as of the end of the fiscal year, including data on exercise price and expiration date. Hence, we no longer need to use the Core and Guay approximation method for post-2006 data. 16 We replicate our main regression for the 4-year time frame: Row 1 of Table IV reports the results. The coefficient on Luck Bad Luck is statistically insignificant. The results indicate that our failure to observe pay for luck asymmetry is not driven by the use of the Core and Guay methodology. Second, for our sample, we design additional tests. The Core and Guay approximation involves first estimating an average per-share intrinsic value (=(S X)) for both vested and unvested option portfolios by dividing the reported aggregate intrinsic value (=ΣN(S X)) by the number of options (=ΣN) in that portfolio, and then subtracting this per-share intrinsic value from the stock price (=S) to arrive at the average exercise price (=X). 18 As Core and Guay point out, this methodology effectively assumes that the exercise price of out-of-the-money options equals stock price, and hence this method overstates the value of the option portfolio if there are underwater options. Given the convex relation between option price and stock price, 16 Coles et al. (2010) discuss how to adjust for compensation reporting changes mandated by FAS123R. 17 In 2006, only 85% of the firms reported in the new format. Thus for the remaining 15% of the firms, our estimate of change in firm-related wealth will be measured with error. Hence, we drop these firms for the year The intrinsic value of the newly granted options is subtracted first from the intrinsic value of the unvested portfolio. Similarly, the number of newly granted options is subtracted from the number of options of the unvested portfolio. This is because for the newly granted options, the exercise price is known and does not have to be approximated. For more details, see Core and Guay (2002). 18

20 this overstatement increases as the options get deeper out of the money. Any limitations in the Core and Guay method apply only to estimates of the change in the value of the option portfolio, which in turn is only one of the factors that determine change in firm-related wealth. Options account for 42% of the value of total firm-related wealth, where wealth is defined as sum of value of stock and option portfolios plus non-equity pay (Himmelberg and Hubbard (2000)). This attenuates any potential mis-estimation of change in wealth caused by the Core and Guay methodology. Nevertheless, we are interested in whether this potential measurement error affects our estimate of change in the value of the option portfolio. If all the options at the beginning of the year were in-the-money and the firm had positive returns during the year, then the options at the end of the year are also in the money. Hence the measurement error is relatively low in this case (Core and Guay (2002)). 19 In all other situations, we will have underwater options either at the beginning of the year or at the end of the year, and this will result in our estimate of the change in wealth being underestimated in absolute terms, with the underestimation depending on the extent to which the options are underwater. 20 Therefore, as an alternate way of addressing the shortcoming in the Core and Guay 19 Suppose an executive holds three options with exercise prices of $50, $55, and $60. Assume the stock price (S) is $65. Pre-2006, firms had to report only the intrinsic value of the portfolio, which is $30 in this example. Then the Core and Guay method would estimate the average exercise price (X) as 65 30/3 = $55. The portfolio value is computed as three times the value of an option with X=$55 rather than the summation of the values of three separate options with X=$50, X=$55, and X=$ Assume an executive holds three options with exercise prices of $50, $55, and $60. Assume the stock price (S) was $45 at the end of year 2004 and $65 at the end of year As per the old reporting format the intrinsic value as of 2004 would be reported as zero (since all the options are underwater), and hence the Core and Guay method would estimate the average exercise price (X) in 2004 as 45 0/3 = $45. Assume the true value of the option portfolio is $100. The estimated value will be higher, say, $120. Assume at the end of 2005, the options are in-themoney, and hence the estimated value of the portfolio is close to the true value, of, say, $140. The true estimate of change in firm-related wealth over the year is $140 $100 = $40, but we would wrongly estimate it as $140 $120 = $20. Now, suppose the reverse is true and the options were in the money at the beginning of the year and out of the money at the end of the year, then the true estimate of change in firm-related wealth is $100 $140 = $40, but we would wrongly estimate it as $120 $140 = $20. Thus, the Core and Guay methodology understates, in absolute terms, the true estimate of change in firm-related wealth. 19

21 methodology, we consider only the subsample of firms that had positive returns in any given year. Though there is no guarantee that this sample of firms will have only in-the-money options both at the beginning and the end of the year, measurement error is likely to be lower for this group of firms. Results for this subsample are reported in Row 2 of Table IV. We find no evidence of asymmetry in pay for luck for this subsample of firms. B. Option Compensation and Asymmetry CEO compensation typically includes options, whose values, by definition, have a convex relation with stock price. Therefore, one might expect a non-linear relation in pay for performance. Moreover, this asymmetry in pay for performance will be stronger if the options are near the money and if the options have shorter time-to-maturity. If the CEOs have either deep in-the-money options (which in effect behave like stocks) or deep out-of-the-money options (whose value does not change much with stock price), then we do not expect asymmetry in pay for performance. Similarly, if the options have long time-to-maturity (typical maturity of option grants = 10 years), then there is very little convexity in call price in relation to stock price. 21 The asymmetry in pay for performance will not translate into an asymmetry in pay for luck, however, if (i) luck is not highly correlated with overall performance or (ii) annual pay following poor performance is high enough to compensate for the loss in value of equity holdings. While we find a modestly high correlation between luck and performance (=0.53), it is likely that firms give higher equity awards (and hence higher pay) following poor performance to bring the level of incentives closer to target (Core and Guay (1999)). Thus, we do not expect to find a link between the structure of option compensation and asymmetry in pay for luck. Nevertheless, we estimate the base-case regression for three subsamples: (i) CEOs whose 21 We thank Rajesh Aggarwal for this comment. 20

22 option portfolio constitutes a significant component of their wealth, (ii) CEOs whose option portfolio consists primarily of near-the-money options, and (iii) CEOs whose options have low time-to-maturity. To identify the sample for (i), we first compute the option ratio as the ratio of the value of the option portfolio to the CEO s firm-related wealth. Wealth is defined as the sum of the values of the stock and option portfolio and the annual non-equity pay (Himmelberg and Hubbard (2000)). We estimate our base-case specification for CEOs that have an option ratio in the top quintile (80 th percentile value of option ratio = 69%). Row 3 of Table IV reports the results. Even for CEOs with high option ratio, we find the coefficient on Luck Bad Luck to be indistinguishable from zero, implying that there is no asymmetry in pay for luck. We find similar results if we use the 90 th percentile as the cutoff. To identify the sample for (ii), we estimate the moneyness of the option portfolio. As pointed in the previous subsection, the estimate of moneyness is precise only for the post-2006 period. We consider CEOs that have an average ratio of stock price to exercise price (S/X) between 0.8 and 1.2 as having near-the-money options. Row 4 of Table IV presents the results. The coefficient on Luck Bad Luck is insignificant, indicating that there is no asymmetry in pay for luck even for CEOs with near-the-money option portfolios. For the data, following Core and Guay methodology, we are able to estimate the moneyness for each tranche of option grants made during the year, but only the average moneyness of the previously granted unvested and vested option portfolios. As before, we define the CEO s option portfolio as being near the money if the average S/X is between 0.8 and 1.2. Row 5 of Table IV presents the results. We continue to find no evidence of asymmetry in pay for luck for this subgroup. For both the post-2006 data as well as the data, we also try other definitions of 21

23 near-the-money options, such as S/X between 0.7 and 1.3, and S/X between 0.9 and 1.1. Our results (untabulated) are qualitatively the same. Lastly, to identify the sample for (iii), we compute the weighted average maturity of the options held by the CEO in each year, using the number of options in each tranche as the weight. We do this only for the post-2006 sample because we can get precise estimates of maturity. We define option portfolios as having short time-to-maturity if the weighted maturity of the portfolio is below the 20 th percentile value. Row 6 of Table IV presents the results. We continue to find no asymmetry in pay for luck. C. Alternative Measures of Luck and Alternative Specifications for Pay-for-luck To make reliable inferences on pay for luck, it is important to estimate luck and skill as precisely as possible. As GM (pg. 215) acknowledge: an alternative explanation for the finding that executives are not fully insulated from bad luck is measurement error in the first-stage decomposition of performance into luck and skill we could get our results simply by misclassifying some skill as luck and vice versa. The average skill estimated using the GM/GMS methodology, is negative ( $398M versus total dollar returns of $548M). The inference that CEOs of S&P 1500 firms, on average, lose $398M each year suggests that measurement error in the GM method may be non-trivial. This measurement error, in turn, could arise from two limitations in the GM/GMS methodology to compute Luck and Skill. We discuss these limitations below and propose three alternative measures of luck and skill. The first limitation is that while the correlation between Luck and Skill should theoretically be zero, we find a high negative correlation. This could arise because the GM methodology requires (i) that the regression be estimated without an intercept term, and, (ii) that the predicted and residual values from the regression of annual stock returns on industry returns 22