The Role of Stock Liquidity and Stock Return Volatility in Executive Compensation: Risk versus Information

Transcription

1 The Role of Stock Liquidity and Stock Return Volatility in Executive Compensation: Risk versus Information Sudarshan Jayaraman and Todd Milbourn Draft Date: July 1, 2009 Abstract We examine how managerial incentives are affected by two equity market trading characteristics stock liquidity and stock return. We find that pay-for-performance sensitivity (PPS) is, in general, increasing in stock liquidity. However, when greater stock liquidity is seemingly due to non-informational trading, we find that it is associated with lower PPS. In terms of stock return, while some studies suggest that greater idiosyncratic is simply noise, others argue that it represents more firm-specific information. Our empirical tests attempt to disentangle the two effects and their relation with PPS. We introduce earnings as a measure of operating risk (noise), thus allowing idiosyncratic to mainly capture the effect of information. We then find evidence that idiosyncratic is positively associated with PPS, but only for smaller firms where the information effect is strongest. Overall, our study provides further insights about the role of risk and information in managerial incentives. Olin Business School, Washington University in St. Louis, Campus Box 1133, One Brookings Drive, St. Louis, MO Contact author: milbourn@wustl.edu. We appreciate helpful comments from Long Chen, Gerald Garvey and Kartik Raman. Any remaining errors are our own.

2 1. Introduction One of the key facets of agency theory is how risk and information shape incentive contracts. In the seminal theories of Holmstrom (1979) and Holmstrom and Milgrom (1987), the optimal compensation weight placed on the manager s output as a signal of her effort depends on the signal-to-noise ratio. The general idea is that an increase in risk (noise) reduces the signal-to-noise ratio while greater information about the manager s actions (signal) increases it. The natural prediction is then that the pay-for-performance sensitivity should be decreasing in the riskiness of the manager s output since it is a noisier measure of her effort in riskier (or more uncertain) environments. Analogously, if there is greater information about the manger s actions in the output, pay-for- performance sensitivity should be higher. A natural environment for testing this basic prediction is the CEO labor market for publicly-held firms. Remuneration data are abundant for these agents, and the firm s stock price serves as a natural measure of output. 1 In situations where a firm s stock price is noisier, pay-for-performance sensitivities should be lower. In contrast, in situations where the firm s stock price is more informative, empirically-observed pay-for-performance sensitivities should be higher. While such a prediction appears straightforward, the empirical issue as to how to identify situations of increased noisiness versus increased informativeness is complex, and one that we attempt to take up in this paper. To guide us in this task, we turn first to market microstructure theory, where the informativeness of market prices is of primary interest. In these models, we see that noise and information are intricately linked. That is, the extent of information revealed in prices as a result of informed trading is naturally a function of the noise inherent in stock prices. A 1 There are numerous empirical studies of the observed pay-for-performance relationship involving stock price, and Aggarwal and Samwick (1999) and Lambert and Larcker (1987) are arguably among the first extensive empirical examinations of how pay-for-performance sensitivity relates to stock price risk. 1

3 sufficient volume of liquidity trading (which is noise by definition) is necessary to attract informed investors to the market as they seek out informational rents, thereby allowing for information to be revealed through prices. Consequently, the implications for stock-based incentive contracting in light of this noise versus information tradeoff are mixed. As a starting point, we first delineate the three leading theoretical predictions relating to stock price informativeness and its effect on compensation contracts. First, in the classic market microstructure models of Grossman and Stiglitz (1980) and Kyle (1985), the marginal benefit of trading on private information is higher in places where stock prices reveal less information. Holmstrom and Tirole (1993) document how greater stock liquidity due to uninformed traders introduces randomness into stock prices, thereby drawing in more informed traders who trade on their private information. In equilibrium, this greater amount of information-based trading results in greater stock price informativeness on average when stock liquidity is higher. Next, Calcagno and Heider (2007) show that having multiple informed traders and/or reducing the horizon of the informed traders can result in equilibria where greater stock liquidity reduces stock price informativeness. Stock price informativeness decreases because the increase in uninformed trading is greater than the increase in informed trading. 2 Further, Paul (1992) shows that when informed traders do not collect information directly related to the manager s effort, greater informed trading need not increase the usefulness of stock prices for managerial incentives. 3 2 See De Long, Shleifer, Summers and Waldmann (1990) for a general model of how informed traders short horizons generate noise trader risk in financial markets. 3 Another possibility that arises in models with a fixed number of informed traders and fixed precision of private information (e.g., Kyle (1985)) is that stock price informativeness does not depend on stock liquidity. This is because more uninformed trading is perfectly offset by more informed trading (see 2

4 Lastly, Ferreira et al (2008) model private benefits as a function of stock price informativeness and find that greater stock price informativeness results in lower pay-forperformance sensitivity. The idea is that an informative stock price mitigates agency conflicts and thus reduces the need to align the agent through equity compensation. Summing up these three branches of the literature, the relation between pay-for-performance sensitivity (PPS) and stock liquidity is ultimately driven by the extent to which increased stock liquidity actually allows for greater informational trading. Our paper seeks to shed light on this subtle relationship. Our first research question examines the overall role of stock liquidity in managerial incentives. First, using turnover as a proxy for stock liquidity, we find that firms with greater stock liquidity rely more on the stock price to remunerate their managers. This result supports the prediction of Holmstrom and Tirole (1993) suggesting that greater stock liquidity increases the amount of information (about the manager s actions) impounded in the stock price, thereby increasing PPS. To rule out the possibility that our results might be due to investor myopia in more liquid stocks, we include earnings as an additional performance measure (e.g., Bankar and Datar (1989), Lambert and Larcker (1987), Sloan (1993)). While the weight on stock price is increasing in stock liquidity (consistent with the information story), there is no evidence that investors place more weight on earnings when liquidity is high (inconsistent with the myopia story). 4 Second, we attempt to isolate situations where higher stock liquidity due to uninformed trading does not necessarily bring in more informed trading and as a result, reduces stock price Admati and Pfleiderer (1988)). Such a result disappears, however, if there are costs to becoming informed. 4 The relation between stock liquidity and PPS is robust to alternate definitions of alignment such as the Core and Guay (2002a) measure of stock option delta and the proportion of annual stock option grants to total compensation. 3

5 informativeness. In particular, we examine the PPS of firms added to the S&P 500 Index since prior research suggests that addition to the Index reduces the amount of firm-specific information that is impounded in stock prices. For example, Barberis, Shleifer and Wurgler (2005) and Vijh (1994) find that stock prices of added firms start co-moving more with the Index and thereby contain less firm-specific information. Addition to the S&P 500 Index provides a natural setting where the firm experiences an increase in stock liquidity but a decrease in price informativeness. Consistent with the prediction in Calcagno and Heider (2007), we find a decrease in PPS after the firm is added to the S&P 500 Index, suggesting that firms where higher stock liquidity is not associated with greater stock price informativeness place less weight on the stock price to remunerate the manager. Third, we use decimalization as a natural experiment to examine how an exogenous increase in stock liquidity affects PPS. Chordia et al (2008) find that decimalization increases the informational efficiency of stock prices. In this setting, we find that PPS increases after decimalization. We argue that these latter two findings sharpen the results provided by Garvey and Swan (2002) and Kang and Liu (2006) that uncover a positive relationship between stock price informativeness and PPS. Our second research question examines the role of stock return in managerial incentives. Prior studies in the compensation literature (e.g., Aggarwal and Samwick (1999)) document a negative relation between PPS and the of dollar returns. Garvey and Milbourn (2003) extend this result by decomposing total dollar into its systematic and idiosyncratic components and show that the negative association between PPS and total dollar comes from the idiosyncratic (i.e., firm-specific) component. These studies interpret their results as consistent with the tradeoff between risk and incentives where greater (dollar) 4

6 stock return indicates greater risk. 5 Other studies have also interpreted idiosyncratic stock return as a proxy for risk or uncertainty. For example, Demsetz and Lehn (1985) use idiosyncratic as the measure of uncertainty of the environment. Similarly, Irvine and Pontiff (2008) show that the increase in idiosyncratic stock return over time (documented by Campbell, Lettau, Malkiel and Xu (2001)) is due to an increase in cash flow. They argue that more intense product market competition has made the operating environment of individual firms more uncertain, and thereby increased idiosyncratic. Thus, according to these studies, idiosyncratic captures uncertainty, which compensation folks equate to noise. However, another research strand characterizes idiosyncratic stock return as measuring stock price informativeness. In an early paper, Roll (1988) analyzes the reasons for low R 2 from a regression of firm returns on market and industry portfolio returns. He conjectures that the low R 2 could be due to one of two reasons (i) private information being impounded into stock prices and/or (ii) occasional frenzy unrelated to concrete information. Subsequent studies have shown that greater idiosyncratic captures more firm-specific information in stock prices. 6 As idiosyncratic has embedded in it the characteristics of uncertainty as well as of information, our second research question attempts to decompose these individual effects to better understand the role of stock return in executive compensation. We do so in two ways. First, we include earnings as an additional 5 Garvey and Milbourn argue that systematic is on average rewarded with higher returns, and thus PPS should not be reduced in the face of higher systematic risk. That said, no such compensation is awarded by financial markets for bearing idiosyncratic risk. Thus, idiosyncratic risk imposes more risk on the agent and PPS should be decreasing in it. 6 See Morck, Yeung, and Yu (2000), Durnev, Morck, and Yeung (2004), Durnev, Morck, Yeung and Zarowin (2003), Chen et al (2007), Fernandes and Ferriera (2008) and Hutton et al (2008). 5

7 variable to capture the uncertainty of the underlying operating environment. 7 Second, we interact stock return (dollar) with proxies for firm size. We discuss our motivations behind each of these two approaches below. We argue that earnings is a cleaner proxy of the uncertainty of the operating environment because it does not suffer from the confounding effects of information as does stock return. The argument is that the information effect is driven by informed traders gathering and trading on their private information in the equity market and impounding this information into the stock price. The of the firm s earnings should not be affected by informed trading incentives. 8 Including both earnings and stock return in the regression model allows earnings to capture the effect of uncertainty, with stock return capturing the residual effects of information. As Earnings captures operating uncertainty, we expect PPS to be decreasing in Earnings. 9 We find a strong inverse relation between earnings and PPS, consistent with greater Earnings capturing uncertainty of the operating environment. 10 Further, we find some evidence that greater stock return is positively associated with PPS once we control for earnings. However, this result needs to be interpreted cautiously because the positive relation is found only in the median regression and not the OLS specifications. 7 While studies such as Lambert and Larcker (1987) and Sloan (1993) examine how the ratio of earnings to stock price affects the weights placed on earnings and stock prices, our focus is on disentangling the individual roles of information and of risk inherent in stock return. 8 While it is true that the incentives to gather and trade on private information is higher in more uncertain environments (i.e., for firms with greater earnings ), this higher information-based trading gets impounded into the stock price and is captured by greater stock return. 9 On the other hand, it is possible that Earnings is a measure of the manager s effort and captures information rather than operating uncertainty. In this case, the weight on the performance measure should be higher when earnings are more volatile. We allow the data to determine which of these effects dominates the other. 10 When we include Earnings as an additional performance measure, the weight on Earnings is also decreasing in Earnings. This reinforces our interpretation that Earnings captures uncertainty, thereby reducing reliance on the stock price (and earnings) as a measure of performance. 6

8 Our second test aimed at understanding the effects of idiosyncratic on PPS relies on interactions of stock return (dollar) with firm size. The more stock prices move because of impounding new information about the manager s actions, the greater is the pay-for-performance-sensitivity (we refer to this as the incentive effect). However, when movements in stock returns result in large swings in the wealth of the CEO, the costs of CEO risk-aversion may kick in and attenuate the greater reliance placed on stock prices for managerial incentives (we call this the risk-aversion effect). To capture the above tradeoff between the information and risk-aversion effect, we allow the relation between idiosyncratic and PPS to vary with firm size. As fluctuations in CEO wealth are greater for large firms, we expect the risk-aversion effect to be dominant in large firms and the information effect to be more important in small firms. Consistent with our prediction, we find a positive relation between idiosyncratic stock return and PPS for small firms. Further, we find that this positive relation gets attenuated as firm size increases, consistent with the risk-aversion effect dominating the information effect for large firms. Overall, our results suggest that the relation between stock return and PPS depends on the relative importance of risk versus information. It is important to point out that while earlier studies, such as Baker and Hall (2004), examine the effect of firm size on PPS, our results elucidate the role of firm size in the relation between idiosyncratic and PPS. In summary, an exploration of the relationship between stock liquidity, stock return and pay-for-performance sensitivity is important because agency theory offers differential predictions related to how risk and information affect managerial pay. Greater risk requires the firm to pay a higher average wage to the executive, while more informative outputs (like price) lower risk and ultimately reduce the optimal wage. Further developing our 7

9 understanding of the tradeoff between risk and information is therefore critical to designing an optimal incentive contract. The rest of the paper is arranged as follows: Section 2 presents the research design followed by a delineation of the role of stock liquidity in managerial incentives. Section 3 examines the role of stock return in pay-for-performance sensitivity (PPS) by first replicating the results of prior studies. We then introduce our tests that seek to isolate the effects of uncertainty and information. Section 4 presents robustness tests followed by concluding remarks in Section Research design 2.1. Data and descriptive statistics Our data come from three sources. Stock liquidity and stock return data are from CRSP; earnings and sales data come from the merged CRSP/Compustat database; and compensation data are from Standard and Poor s ExecuComp database. Our sample period is from 1992 to 2006, beginning in the first year of the ExecuComp data and ending the last year of the merged CRSP/Compustat database. Our study uses 2,680 large U.S. firms resulting in 20,546 firm-year observations with non-missing data for all variables. Table 1 summarizes the basic variables of interest. The average CEO receives an annual salary and bonus that both average around $626,000 and $655,000 per year, respectively. The average annual Change in CEO wealth (defined as total annual compensation plus change in the value of shares and options) is approximately $10 million dollars, of which roughly $4 million is from annual compensation. These data reaffirm that changes in equity-based compensation are responsible for a large portion of the change in the CEO s wealth. There is a large cross-sectional variation in Change in CEO wealth with the largest decline of $145 million and the largest gain of 8

10 around $300 million. The decomposition of total returns into systematic and idiosyncratic returns is done using the preceding five years of monthly data (consistent with Aggarwal and Samwick (1999) and Garvey and Milbourn (2003)). Annual firm-level estimates are calculated using rolling windows of 60 months. The betas are estimated using an OLS regression of log returns on the value-weighted CRSP index. 11 Systematic and Idiosyncratic measure the standard deviation of systematic and idiosyncratic returns, respectively. We use log turnover (Turnover) defined as the log of the ratio of total shares traded monthly divided by shares outstanding as the proxy for stock liquidity (see Lo and Wang (2000) for a description of various measures of trading volume). 12 To maintain comparability with the stock return measures, we compute Turnover as the average of the last five years monthly measures. However, our results are robust to using annual measures of Turnover. Earnings is defined as the standard deviation of five annual earnings before extraordinary items. Tobin s Q is the ratio of market value to book value of assets. Firm size is denoted by the log of annual sales (Log sales). All variables have been winsorized at the one percent tails to reduce the influence of outliers. Table 2 presents the spearman correlation between the variables. Total compensation, two of the components of Total compensation (viz., Salary and Bonus), and Change in CEO wealth are all positively related to one another and to firm size (both to Market cap as well as Log sales). Larger firms have lower Systematic, lower Idiosyncratic and lower Turnover. Further, Idiosyncratic and Turnover are positively related, suggesting that firms that trade more heavily have more volatile idiosyncratic returns. We are, however, more interested 11 Using the S&P 500 Index return yields similar results. 12 Our inferences are similar when we use alternate measures of stock liquidity such as the bid-ask spread. 9

11 in how the relation between pay and performance varies across the sample as a function of stock liquidity and stock return, which is the focus of the next sections Relation between stock liquidity and PPS A large literature in information economics examines the interaction between informed traders (those who trade on information) and uninformed traders (those who trade for liquidity reasons), and the ultimate effect of this interaction on stock price informativeness. Several studies have investigated how stock price informativeness is influenced by the amount of stock liquidity. While most models generally agree that more uninformed trading attracts more informed trading, there is no consensus about the equilibrium effect of this interaction on stock price informativeness. As argued, this effect plays a key role in predicted levels of PPS. As is standard in the executive compensation literature (e.g., Jensen and Murphy (1900)), we regress the Change in CEO wealth on Stock price Performance (defined as Stock return * Market cap) and denote the coefficient on Stock price Performance as the measure of the pay-forperformance sensitivity (PPS). To examine the relation between PPS and Turnover, we create the cumulative distribution function of Turnover (CDF of Turnover) and interact it with Stock price Performance. A positive (negative) coefficient of this interaction term indicates that PPS is pronounced (attenuated) for firms with greater stock liquidity. If stock liquidity improves stock price informativeness and thereby increases the marginal benefit of PPS according to the prediction in Holmstrom and Tirole (1993), we expect the coefficient of Stock price Performance * CDF of Turnover to be positive. On the other hand, theories such as Paul (1992) and Calcagno and Heider (2007), where greater stock liquidity lowers stock price informativeness either because informed traders are gathering information that is not relevant to the manager s effort or because of free-rider problems amongst multiple informed traders, we expect the coefficient 10

12 of Stock price Performance * CDF of Turnover to be negative. We would also expect a negative coefficient if greater stock liquidity improve stock price informativeness but acts as a substitute for managerial incentives (as in Ferreira et al (2008)). We use three empirical specifications to test the above predictions. Model 1 presents results from a median regression. Model 2 estimates an OLS regression with year and industry fixed effects, while Model 3 includes executive fixed effects in addition to the year and industry fixed effects. As is standard, we include proxies for growth opportunities (Tobin s Q) and firm size (Log sales) as additional controls. For example, Bizjak, Brickley and Coles (1993) find that PPS is increasing with Tobin s Q, while Jensen and Murphy (1990), Jin (2002), Milbourn (2003) and Baker and Hall (2004) find that PPS is decreasing in firm size. Panel A of Table 3 presents results of the role of Turnover in the relation between pay and performance. The coefficients on Stock price Performance * CDF of Turnover are positive and significant in all three specifications. Greater stock liquidity appears to be associated with greater stock price informativeness and thus increases the reliance that firms place on the stock price as a signal of the manager s effort. The evidence supports the prediction of Holmstrom and Tirole (1993) and suggests that firms rely more on stock prices to compensate their CEO when liquidity is high. The results for control variables are consistent with prior studies Stock price and earnings as multiple performance measures An alternative explanation for the increased weight placed on the stock price in more liquid firms is investor myopia (see Stein (1988, 1989)). 13 If greater liquidity is associated with more myopic investors, then the increased weight on the current stock price might be designed 13 Garvey, Grant and King (1998, 1999) endogenize the manager s concern over short-term stock prices and characterize the resulting contracting implications. 11

13 to make the CEO care more about the short-run price, and not necessarily due to a more informative stock price. To examine this alternative, we include earnings as an additional performance measure as in Banker and Datar (1989). If more liquid firms are characterized by greater myopia, we would expect a higher loading on earnings. On the other hand, if greater stock liquidity is associated with more informative stock prices, we would not expect the weight on earnings to be increasing in stock liquidity. 14 Following Jensen and Murphy (1990), Lambert and Larcker (1987) and Sloan (1993), we define Earnings performance as the change in earnings before extraordinary items. Although our main coefficient of interest is the interaction of Earnings performance with the CDF of Turnover (Earnings performance * CDF of Turnover), we also include interactions of Earnings performance with the CDFs of Tobin s Q and Log sales in the empirical model. Results are presented in panel B of Table 3. The coefficient on the interaction term Earnings performance * CDF of Turnover is negative and significant in the median regression, but insignificant in the OLS regressions. Further, the coefficients of Stock price Performance and Stock price Performance * CDF of Turnover remain positive and significant in all three specifications. Overall, there is no evidence that firms place more weight on earnings in more liquid firms, which appears to be inconsistent with the investor myopia story and thereby buttressing our interpretation of the findings PPS before and after S&P 500 Index additions To explore whether liquidity necessarily translates to informativeness, we estimate how the PPS is affected by a firm s addition to the S&P 500 Index. Several studies have found that 14 One could argue that the weight placed on earnings should be decreasing in stock liquidity as firms substitute stock based measures for earnings based performance as the precision of the former increases. We do not make this prediction as the multiple performance measure theory makes predictions about the ratio of the weights on the performance measures and not about the individual weights. 12

14 firms added to the S&P 500 Index experience a significant increase in stock liquidity (e.g., Beneish and Whaley (1996), Hegde and McDermott (2003) and Kaash (2007)). These increases in liquidity are associated with increases in index fund following, institutional trading and also greater retail investor following. However, Vijh (1994) and Barberis et al (2005) find that stock prices of firms added to the S&P 500 Index experience greater co-movement with the Index, which suggests that they contain less firm-specific information after addition to the Index. We examine the PPS of managerial compensation before and after a firm is added to the S&P 500 Index. As additions are associated with increases in stock liquidity but decreases in price informativeness, this offers us a natural experiment to examine the conflicting predictions about the role of stock liquidity in executive compensation. Our sample of S&P 500 Index additions are from 1992 to 2006 and are obtained from two sources Barberis et al (2005) for additions from 1992 to 2000 and directly from S&P for 2001 onwards. 15 The final sample contains 2,386 firm-year observations for 236 additions. We define an indicator variable, Post_S&P_Addition, that takes the value of one in the post-addition period and zero in the preaddition period. We interact Stock price Performance with Post_S&P_Addition. If the estimated PPS decreases (increases) after S&P 500 Index additions, we expect the coefficient of Stock price Performance * Post_S&P_Addition to be negative (positive). Table 4 presents results of the above regression. The coefficient on Stock price Performance * Post_S&P_Addition is negative and significant in all three specifications. 16 This suggests that PPS is lower after S&P 500 Index additions, consistent with the drop in stock price informativeness after S&P 500 Index additions. These results are also consistent with Calcagno and Heider (2007) as they show that instances where greater stock liquidity is associated with Including Earnings performance and the interaction Earnings performance * Post provides similar results. 13

15 greater uninformed trading (relative to informed trading) reduce stock price informativeness and are therefore associated with lower PPS PPS before and after decimalization In a similar vein, we explore changes in PPS around an exogenous shock to stock liquidity via the decimalization of the bid-ask spread. Chordia et al. (2008) use decimalization of the spread as an exogenous increase in stock liquidity and find that market efficiency increased in the post-decimalization period. Following Chordia et al., we define an indicator variable (Decimal) to denote the period after January To examine the change in PPS after decimalization, we interact Stock price Performance with Decimal. To ensure that the effect of decimalization is not confounded by other regulatory changes such as the passing of the Sarbanes-Oxley Act (in 2003), we retain firm-year observations until the end of year Table 5 presents the results. The coefficient of Stock price Performance * Decimal is positive and significant in both model 1 (median regression) and model 3 (OLS with fixed effects), which suggests that the post-decimalization period is associated with higher pay-for-performance sensitivity. 17 Overall, the evidence suggests that an exogenous increase in stock liquidity as a result of decimalization increases PPS, which we argue is due to an increase in informativeness. 3. Role of stock return in PPS In this section, we seek to understand the effects of increased idiosyncratic stock return on observed PPS levels by relying on the same information versus noise lens. We begin by confirming the empirical relationship identified in the literature. 17 When the entire sample (including post-2002 period) is used, the coefficient of Stock price Performance * Decimal remains positive and significant in model 1 and insignificant in model 2. However, it becomes insignificant in model 3. 14

16 3.1. Stock return and PPS We first document the relation between systematic and idiosyncratic of dollar returns and PPS by replicating the results of Garvey and Milbourn (2003) for our sample. To examine the relation between PPS and both Systematic and Idiosyncratic, we create the cumulative distribution function of Systematic (CDF of Systematic ) and of Idiosyncratic (CDF of Idiosyncratic ) and interact each of these with Stock price Performance. Garvey and Milbourn (2003) find a negative coefficient of Stock price Performance * CDF of Idiosyncratic and an insignificant coefficient of Stock price Performance * CDF of Systematic. Table 6 presents results of the roles of Systematic and Idiosyncratic in the relation between pay and performance. 18 Panel A reports results based on dollar risk while Panel B presents results based on percent risk as in Core and Guay (2002b). Relying on dollar, the coefficients of Stock price Performance * CDF of Idiosyncratic are negative and significant (at less than the one percent level) in all three specifications. Thus, pay-forperformance sensitivity is decreasing in idiosyncratic dollar return, consistent with the results in Garvey and Milbourn (2003). Further, the coefficient of Stock price Performance * CDF of Systematic is insignificant in all three specifications, confirming the inference of prior studies that systematic risk is not removed for the average CEO. 19 The explanatory power of the three models is 0.16, 0.30 and 0.31, respectively. Panel B presents results based on of percent returns. Contrary to the results based on dollar risk, we find a positive and significant coefficient of both Performance * CDF of 18 We do not include stock liquidity as an additional determinant in these specifications to enable comparisons with prior research. However, we verify, in unreported tests, that our inferences are robust to including stock liquidity. 19 See Gopalan, Milbourn and Song (2009) for recent work on this issue. 15

17 Systematic and of Performance * CDF of Idiosyncratic in all the three specifications. This seems to suggest that there is a positive association between of returns and PPS when percent returns (instead of dollar returns) are used. See also Core and Guay (2002b) and Aggarwal and Samwick (2002) for related discussions on the role of dollar return versus percent return in estimating PPS Disentangling the individual effects of information and risk Along the line of the analysis above, the existing executive compensation literature has examined the link between PPS and idiosyncratic solely as a test of how increased risk (uncertainty) caused by such firm-specific events affects the observed PPS. However, in the asset pricing literature, several studies, beginning with Roll (1988), argue that idiosyncratic return captures the amount of firm-specific information in prices. As idiosyncratic potentially incorporates the effects of both information and uncertainty, we attempt to delineate these individual effects to gain further insights into the role of stock return in managerial incentives. We do so in two ways. First, we include earnings as an additional proxy to capture the uncertainty of the operating environment (in Section ). Second, we interact stock return with firm size in Section to tease out the effect of firm size on the relation between PPS and idiosyncratic return Role of earnings in the relation between stock return and PPS 20 Core and Guay (2002b) and Aggarwal and Samwick (2002) also highlight the importance of controlling for firm size in PPS regressions. All our empirical specifications use Log sales to control for firm size. Further, as results may vary depending on whether or not the sample contains firms with less than 48 monthly observations (Aggarwal and Samwick (2002)), we re-run all our results based on a smaller sample of firms with a minimum of 48 monthly observations. These tests are presented in Section 4. 16

18 Irvine and Pontiff (2008) recently argue that the increase in idiosyncratic of stock returns over time (first documented by Campbell, et al (2001)) can be attributed to the increase in the of underlying earnings (and cash flows) of the firm. Irvine and Pontiff argue that uncertainty of the operating environment (caused by increasing product market competition) can explain the increasing trend in idiosyncratic of returns over time. Thus, we introduce the of the firm s earnings (Earnings ) as an additional determinant of PPS. Our motivation for this empirical strategy is as follows. Earnings is arguably a cleaner proxy for the uncertainty of the operating environment because it does not have the potentially confounding effects of information inherent in Idiosyncratic. Recall that the information effect arises based on informed traders trading on their private information in the equity market and impounding this information into the stock price. The of the firm s earnings is not affected by informed trading incentives and should, therefore, be unaffected by the information effect. Thus, by including both Earnings and Idiosyncratic in the same specification, we allow Earnings to capture the effect of uncertainty, while allowing Idiosyncratic to capture the residual effect of information. We expect PPS to be negatively related to Earnings. On the other hand, if Earnings conveys information about the manager s actions not contained in stock price, PPS will be higher when earnings are more volatile. We now turn to the data to determine which of these effects dominates. Table 7 presents the results of the relation between PPS and Earnings. Panel A includes Stock price as the performance measure, while panel B relies on Stock price as well as Earnings. To mirror the definition of dollar risk, Earnings is defined as the of total earnings. The coefficient of Stock price Performance * CDF of Earnings is negative and significant in all three specifications in panel A. Both the economic and the statistical 17

19 significance of Earnings in influencing PPS are strong. The effect of Earnings on PPS is stronger than that of firm size (Log sales) in the two OLS specifications. This result suggests that Earnings captures of the operating environment and thus reduces the reliance placed on stock prices to remunerate the manager (consistent with the results for Idiosyncratic documented in Section 3 and in Aggarwal and Samwick (1999) and Garvey and Milbourn (2003)). Interestingly, the coefficient of Performance * CDF of Idiosyncratic is now positive and significant (at the one percent level) in the median regression. This result suggests that once Earnings is included in the regression specification to control for the uncertainty (noisiness) of the operating environment, Idiosyncratic captures the residual effect of information and is thus positively associated with PPS. However, one has to be cautious while making this interpretation as the positive coefficient is found in only one out of the three specifications. Results are similar in panel B that includes Stock price and Earnings. In particular, the coefficient of Stock price Performance * CDF of Earnings is negative and significant in all three specifications. The coefficient of Earnings Performance * CDF of Earnings is also negative in all three models, but is statistically significant in only the median regression. The coefficient of Stock price * CDF of Idiosyncratic remains positive and significant in the median regression. Overall, there is some evidence that Idiosyncratic is positively associated with PPS once of the operating environment is controlled for using Earnings. Further, the negative relation between Earnings and PPS is consistent with the inverse relation between risk and incentives Role of firm size in the relation between PPS and Idiosyncratic 18

20 Our results suggest that the empirical relation between stock return and PPS is the outcome of the tradeoff between information and risk. The more stock prices move due to new information being impounded, the more they should be used in incentive contracts (the information effect). However, when these movements in stock prices result in large swings in the CEO s wealth, her aversion to fluctuations in wealth (the risk-aversion effect) may start to kick in. This risk-aversion effect leads to an attenuation of the information effect. Consistent with the latter rationale, Aggarwal and Samwick (1999) argue that the appropriate proxy to capture the extent of risk placed on the agent is the of dollar returns. The idea is that as a 1% return results in a greater fluctuation in the wealth of the CEO of a Fortune 500 company versus that for the CEO of a start-up, what is important is the of dollar returns. Evidence in Panel A of Table 6 and panels A and B of Table 7 support their argument. As the attenuation effect due to CEO risk-aversion is expected to be pronounced for large firms, we capture the above tradeoff between the information effect and the risk-aversion effect by allowing the relation between PPS and Idiosyncratic to vary depending on firm size. In particular, we interact Stock price Performance * CDF of Idiosyncratic with CDF of Log sales. As the information effect is expected to dominate the risk-aversion effect for small firms, we expect the coefficient of Stock price Performance * CDF of Idiosyncratic (which captures the relation between PPS and Idiosyncratic for the smallest firm in the sample) to be positive. As the risk-aversion effect is expected to overwhelm the information effect as firm size gets larger, we anticipate that the coefficient of the interaction term (Stock price Performance * CDF of Idiosyncratic * CDF of Log sales) will be negative. Further, we also interact firm size with CDF of Earnings and with CDF of Systematic. Table 8 presents these results. Consistent with the tradeoff between information and risk, the coefficient of Stock price Performance * CDF of Idiosyncratic is positive and 19

21 significant in all three specifications. This result suggests that of dollar returns is positively associated with incentives in small firms where the information effect is expected to dominate the risk effect. Further, the coefficient of Stock price Performance * CDF of Idiosyncratic * CDF of Log sales is negative and significant in all three specifications, suggesting that the positive effect of idiosyncratic on incentives gets attenuated as the size of the firm gets larger. The coefficient of this interaction term is larger than that of Performance * CDF of Idiosyncratic, which indicates that the risk-aversion effect dominates the information effect for the largest firm in the sample. 21 These results document the importance of firm size in understanding the relation between stock return and PPS. While prior studies (e.g., Schaefer (1998), Baker and Hall (2004)) examine the relation between PPS and firm size, our results provide evidence on how firm size affects the relation between PPS and idiosyncratic. These analyses provide new insights about the tradeoff between risk and information. 4. Robustness tests In this section, we put our findings up against a battery of robustness tests Smaller sample with minimum 48 monthly observations Aggarwal and Samwick (2002) show that the relation between dollar return and PPS is sensitive to whether or not the sample contains firms with less than 48 monthly observations to compute the measures (see also Core and Guay (2002b)). We verify whether our results are sensitive to this criterion. Panels A and B of Table 9 present the relation between stock liquidity and PPS and stock return and PPS, respectively, for the smaller sample with at least 48 monthly observations. Our sample size drops from 20,546 to 19,994 observations with this estimation restriction. The coefficient of Stock price 21 We find similar results when we include Earnings and the interaction of all CDFs with Earnings. 20

22 Performance * CDF of Turnover in Panel A is positive and significant in all three specifications, suggesting that our inferences regarding the effect of stock liquidity on PPS is insensitive to this exclusion criterion. Similar to the earlier results for the larger sample, the coefficient of Stock price Performance * CDF of Idiosyncratic in the median regression is positive and significant once earnings is included in the regression. Overall, the relation between stock liquidity, stock return and PPS appears to be fairly robust to the smaller sample of firms for which we have at least 48 monthly observations Alternate measure of Pay-for-Performance Sensitivity Core and Guay s (2002a) delta In this section, we use the measure of the sensitivity of CEO s dollar value of stock options to changes in stock price (DELTA) according to the methodology in Core and Guay (2002a). As DELTA is a direct measure of the pay-for-performance sensitivity, we regress DELTA on CDF of Turnover and controls to examine the role of stock liquidity in managerial incentives. The first three columns in Table 9 present results of the above tests. The coefficient of CDF of Turnover is positive and significant in all three regression specifications, suggesting that the relation between stock liquidity and PPS is robust to using the Core and Guay (2002a) measure of DELTA Annual stock option grants Ferreira et al (2008) argue that boards provide incentives to executives through new option grants. Thus, we examine the robustness of our results to the use of annual stock option grants. To isolate the effect of stock option grants from other components of annual compensation, we compute the proportion of the annual compensation that is comprised of 21

23 stock option grants. 22 In particular, we use the ratio of the Black-Scholes value of annual stock option grants (OPTGRANT) to total annual compensation and examine the relation between OPTGRANT and stock liquidity. Similar to DELTA, we regress OPTGRANT on the CDF of Turnover and controls. Columns 4 to 6 of Table 10 present the results. The coefficient of CDF of Turnover is positive and significant in all three specifications. This suggests that the proportion of the CEO s annual compensation that is comprised of stock option grants is higher in firms with greater stock liquidity. Thus, the relation between stock liquidity and managerial incentives appears to be robust to alternate measures of managerial alignment and the means by which CEOs are compensated with stock-based instruments. 5. Conclusion Our study offers three contributions to the literature. First, it provides empirical evidence regarding the conflicting theoretical predictions of the relation between stock liquidity and pay-for-performance sensitivity. Our results suggest that, in general, greater stock liquidity is associated with greater stock price informativeness and is therefore associated with higher PPS (consistent with Holmstrom and Tirole (1993)). We find that PPS increases after decimalization an exogenous shock to liquidity that increased the informational efficiency of stock prices. However, when greater stock liquidity is associated with non-informational trading, it increases the amount of noise in stock prices and is thus associated with lower PPS (consistent with Calcagno and Heider (2007)). Second, the study adds to our understanding of the relation between stock return and executive compensation by disentangling the effects of information from those of 22 In unreported results, we confirm that our inferences are similar when we use the value of stock option grants. 22

24 risk or uncertainty. Greater stock return incorporates two effects it impounds more information which increases PPS but also results in greater swings in CEO wealth, which reduces PPS. We find that the relative importance of these effects in executive contracts is a function of firm size. Finally, our study uses the setting of managerial incentives to indirectly add to the debate about whether greater idiosyncratic reflects greater uncertainty, or more firmspecific information. While studies such as Campbell et al (2001) and Chordia et al (2008) have documented inter-temporal increases in idiosyncratic and stock liquidity respectively; while others such as Hall and Liebman (1998) have provided evidence of increasing CEO compensation over time, no study has examined the relation between these increases. An interesting extension of our study would perhaps be to analyze the relations between stock liquidity, stock return and CEO compensation over time. 23

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