We examine the role of information-based stock trading in affecting the risk incentive relation. By incorporating

Transcription

1 MANAGEMENT SCIENCE Vol. 56, No. 4, April 2010, pp issn eissn informs doi /mnsc INFORMS Information-Based Stock Trading, Executive Incentives, and the Principal-Agent Problem Qiang Kang School of Business Administration, University of Miami, Coral Gables, Florida 33124, Qiao Liu Faculty of Business and Economics, University of Hong Kong, Pokfulam, Hong Kong, We examine the role of information-based stock trading in affecting the risk incentive relation. By incorporating an endogenous informed trading into an optimal incentive contracting model, we analytically show that, apart from reducing incentives, a greater risk increases the level of information-based trading, which consequently enhances executive incentives and offsets the negative risk incentive relation. We calibrate the model and find that the economic magnitude of this incentive-enhancement effect is significant. Our empirical test using real-world executive compensation data lends strong support to the model prediction. Our results suggest that principals (boards of directors) should consider underlying stock trading characteristics when structuring executive incentives. Key words: risk incentive trade-off; endogenous information-based trading; pay-performance sensitivity; adjusted pin; calibration History: Received April 22, 2008; accepted October 8, 2009, by David A. Hsieh, finance. Published online in Articles in Advance February 12, Introduction A standard principal-agent model predicts a negative relation between risk and incentives (Holmstrom 1979, Holmstrom and Milgrom 1987). Uncertainty of an economy adds observation errors to agents performance measures and dampens agents incentives to act in the principal s best interest. Yet, empirical evidence in support of this prediction is mixed. 1 Theoretically, both Prendergast (2002) and Raith (2003) have argued that the effects of uncertainty on incentives are much more involved: apart from reducing incentives outright, increased uncertainty may also affect incentive provision via other channels. In this paper, we examine the role of informationbased stock trading in affecting executive incentives. We propose that information-based stock trading that is driven by increased uncertainty enhances incentives and complicates the risk incentive relation. All else equal and on the margin, a greater uncertainty attracts more informed stock traders and motivates more information-based trading in the market. As 1 Ittner et al. (2003) document that pay-for-performance schemes are widely used by new economy firms, which arguably have higher risks. Aggarwal and Samwick (1999) and Jin (2002) report a significantly negative relation between CEO incentives and risk. Core and Guay (1999) document a significantly positive relation. Garen (1994) finds no correlation. a result, the stock trading impounds more information into a firm s stock price, which the principal can use to better incentivize his manager. We characterize this information channel of incentive provision due to the heightened uncertainty analytically. We also quantify its economic significance both numerically and empirically. Our motivations for this inquiry are twofold. First, optimal incentive contracting calls for principals to use all useful information. The stock market works as an information aggregator and sends principals meaningful signals to better incentivize executives. The intensity of information production, which is largely determined by stock market microstructure, profoundly affects managerial incentives and potentially sheds light on the risk incentive relation in the principal-agent literature. This perspective has been relatively understudied. Second, our analysis might generate valuable managerial implications. The business world widely uses pay-for-performance schemes to align interests of managers with interests of principals (i.e., shareholders, boards of directors). The efficacy of such incentive mechanism might depend on whether and how much principals consider the business environment, such as the firms risk profile and the characteristics of stock trading, when structuring managerial incentives. Our analysis provides useful evidence from which boards can learn to better manage executive compensation. 682

2 Management Science 56(4), pp , 2010 INFORMS 683 We begin by proposing a model that combines a standard optimal contracting process with a Kyle (1985) type of stock trading process. 2 In our model, the information content in the stock price is endogenously determined and depends only on market characteristics such as risk, liquidity, precision of private signals, and reservation value of becoming an informed trader. We analytically decompose the equilibrium impact of risk on incentives into two offsetting effects: one measures the standard risk incentive trade-off effect given certain amount of information-based trading, and the other reflects the incentive enhancement effect due to the informationbased trading induced by a higher level of risk. An increase in uncertainty, rendering incentives more costly, makes prices relatively more informative by inducing more traders to become informed, which in turn enhances incentives and dampens the negative effect of risk on incentives. We numerically examine the economic significance of the incentive enhancement effect driven by increased information-based trading. Using realworld executive compensation data and stock market data, we calibrate our model with an internally consistent multistep approach. Our calibration analysis demonstrates the following: (1) the pay-performance sensitivity equals 0.042, representing a $42 increase in CEO compensation per $1,000 increase in shareholder value; (2) the manager s disutility (in certainty equivalent measure) from effort equals approximately 2.10% of the average market value; (3) the profit of informed trading is approximately 4.18% of the average market value; (4) approximately 20% of variation in aggregate market orders is due to liquidity orders; and (5) the incentive-enhancement effect due to increased uncertainty offsets 20% 30% of the incentive-reduction effect and contributes significantly to social welfare improvement. We also empirically test our model prediction by using the actual compensation data over We use Duarte and Young s (2009) adjusted probability of informed trading (PIN), which is developed from an extended version of the Easley et al. (1996) 2 Our model shares similar motivations of Holmstrom and Tirole (1993), but there exists one important theoretic difference in the structure of the information market. Their argument relies crucially on the costly collection of private information by a single, large, risk-neutral insider who acts as an information monopolist and chooses the precision of signals impounded into stock prices. Our model assumes a dispersed information market that is open and accessible (with a cost). Because of the competition among informed speculators, the information content in stock prices is endogenously determined by satisfying an equilibrium condition that the marginal profit and the marginal cost of information collection are equal. Moreover, as we elaborate in 2, certain technical features make it less feasible to calibrate Holmstrom and Tirole s (1993) model and to empirically test their model prediction. model, as a proxy for the amount of informationbased stock trading. We decompose this PIN measure into two orthogonal components: one is risk related and the other is not. Using both the median regressions and the ordinary least-square (OLS) regressions with fixed effects, we examine the effects of the two components on CEO incentives. We find that the risk-driven information-based trading leads to improved CEO incentives, partially canceling the reduction in CEO incentives caused by the heightened risk. According to the OLS regression results, a one-standard-deviation increase in risk causes a direct reduction of CEO incentives by $1.506 and an indirect improvement in CEO incentives by $0.656, which represents a 43% offset of the negative risk incentive effect. Using the median regression results, we document that a similar change in the level of risk causes an 80% offset of the negative risk incentive effect. These results have useful managerial implications. Our findings, by pinpointing the impacts of information-based trading on executive incentives, suggest that as long as the underlying stock trading process can impound more information into stock prices, pay-for-performance schemes are still able to incentivize managers, even in an uncertain environment. Traditional incentive pay focuses less attention on differentiating between value created due to market-wide factors and to managerial individual efforts. Executives might be rewarded regardless of their merits e.g., it happened during the stock market run-up of the late 1990s and top-performing executives might be penalized if their tenure coincides with a bear market. Principals can better structure managerial incentives if they actively promote information-based trading and use the information contained in stock prices to filter out factors outside the control of executives and the return expected by shareholders. Another related implication is that incentive pay may not work perfectly to the interests of principals if firms operate in a highly uncertain environment with inefficient stock market information production, e.g., in an illiquid market or an emerging market with a high level of volatility but a low level of information disclosure. An empirical test using international data might help illuminate this point. Our paper contributes to several strands of related literature. First, our paper adds to the burgeoning executive compensation literature in several ways. Empirical studies on executive compensation have exploded since the early 1990s (Murphy 1999), but there has been a paucity of attempts on model calibrations. Lambert et al. (1991) and Haubrich (1994) are among the first to calibrate the agency models. Some recent works include Hall and Murphy (2002), Hall and Knox (2004), and Dittmann and Maug (2007).

3 684 Management Science 56(4), pp , 2010 INFORMS In a framework that embeds endogenous informed trading with executive compensation, we calibrate parameters key to the optimal contracting model and document calibrated values broadly consistent with empirical evidence and in support of the agency theory. Although the bulk of executive compensation is equity based, the linkage of executive compensation to stock trading and stock price informativeness is yet to be mapped out. We fill in the void and illustrate, both theoretically and empirically, the effects of information-based stock trading on managerial incentives and risk incentive relations. Second, our paper is closely related to a large literature that studies the effect of stock price informativeness on corporate actions and corporate control. 3 The theoretical part of our paper is most closely related to Holmstrom and Tirole (1993), but there are some major differences between our model and theirs (see Footnote 2 and 2). Another closely related theoretic work is Faure-Grimaud and Gromb (2004), who show that by impounding more information into a stock price, public trading increases the incentives of a firm s large shareholder ( insider ) to engage in value-increasing activities. Our paper differs from theirs in several ways: They focus on the insider s incentives that are governed by the insider s stake, but we focus on CEO incentives that are structured by the incentive contract; moreover, besides the theoretical reasoning, we also conduct the numerical analysis and empirical tests. There are also several related empirical studies. For example, Chen et al. (2007) empirically show that measures of informed trading have a positive effect on corporate investment. Third, we propose an important channel through which stock market efficiency improves economic efficiency. Dow and Gorton (1997) and Dow and Rahi (2003) emphasize the information role of the stock market in guiding managers investment decisions. We, however, focus on the information role of the stock market in structuring executive incentives. Also, to the extent that executive compensation is one particular corporate governance mechanism, our study explicitly examines the relation between corporate governance and stock market microstructure. The remainder of this paper proceeds as follows. Section 2 characterizes our model and analytically decomposes the risk incentive relation into two offsetting effects. Section 3 conducts the model calibration and the social welfare analysis. Section 4 presents empirical results. Section 5 concludes. 3 Theoretical attempts on this issue include, to name a few, Kyle and Vila (1991), Fishman and Hagerty (1992), Holmstrom and Tirole (1993), Dow and Gorton (1997), Subrahmanyam and Titman (1999), Dow and Rahi (2003), Faure-Grimaud and Gromb (2004), and Edmans (2009). 2. The Model Holmstrom and Tirole (1993) are among the first to combine the stock price formation process with the optimal contracting process. They show that a firm s stock price incorporates performance information that cannot be extracted from the firm s current or future profit data. The amount of information contained in the stock price is useful for structuring managerial incentives. An illiquid market makes the stock price less informative and thus reduces the benefits of stock market monitoring. Although Holmstrom and Tirole (1993) highlight the importance of market microstructure in inducing executive incentives, it is not easy to calibrate their model and build an empirical analysis. 4 We thus introduce a parsimonious model that links the information-based stock trading to an optimal incentive contracting process. We use the model to demonstrate the effects of information-based trading on the risk incentive relation and to motivate our quantitative research in this paper Economy We begin with a single-period model with two points of time, indexed t = 0 1. The period is further divided into several stages. We summarize the time line of the model in Figure 1. At the initial point of time 0, a publicly held firm is established, and shares are issued on the firm s future cash flow. The terminal payoff of the firm at time 1 is r = e +, where e is the earning determined by managerial actions, and is a noise term, representing factors outside the manager s control. We assume that follows a normal distribution with mean zero and variances V. At stage 1, the firm owner (the principal) hires one manager (the agent). The owner writes a compensation contract on two performance measures, the stock price P and the firm s terminal payoff r: W = a + bp + f r (1) where a represents the fixed salary, and b and f capture the sensitivities of the manager s compensation to P and r, respectively. The compensation contract 4 In the Holmstrom and Tirole (1993) model, ownership concentration directly determines market liquidity, which subsequently sets the level of stock price informativeness and pay-performance sensitivity. Hartzell and Starks (2003) report that the ownership structure exerts its impact on pay-performance relation through a corporate governance channel. It is not trivial to disentangle the two incentive effects of ownership. In addition, whereas the traditional principal-agent model treats the volatility as a measure of uncertainty, the Holmstrom and Tirole (1993) model assumes that stock price volatility conveys the precision of informed traders information, which is difficult to quantify. 5 Based on this model, we also develop and empirically test another prediction that information production via stock trading improves executive incentives (see Kang and Liu 2008).

4 Management Science 56(4), pp , 2010 INFORMS 685 Figure 1 The Time Line t = 0: Public firm established t = 1: Terminal payoff realized; incentive contract honored; firm liquidated Time Principal offers incentive contract; manager chooses effort level Stock market opens; informed traders collect costly information; informed and liquidity traders submit orders; stock price set; stock market closes in Equation (1) follows a commonly adopted form in the literature (see, e.g., Holmstrom and Milgrom 1987, Holmstrom and Tirole 1993, Baiman and Verrecchia 1995). Given the compensation contract, the manager chooses an effort level e 0, which is unobservable. 6 At stage 2, the stock market opens. We assume that the manager is barred from trading. 7 A stock market investor can observe an informative but noncontractible signal on the firm s future value at a cost. She does not search for the costly private signal on unless her expected value of doing so exceeds her reservation value. The costly signal acquired by an informed investor i is + i, where i is independent and identically distributed with mean zero and variance V. Informed trader i submits a market order that is linear in her signal, + i. Both informed and uninformed traders submit their orders to the market maker, who cannot tell whether an order is from an informed trader or from an uninformed trader. We assume that the total liquidity demand (of uninformed traders) in the market is z, and z is a normally distributed variable with mean zero and variance V z. We also assume that there are N informed investor, and N is an endogenous number. The total order flow observed by the market maker is = N + N i=1 i + z. The competitive market maker, given the aggregate order flow, sets a price such that P = E r. 8 6 Murphy (1999) provides a criticism on the standard principalagent model. In practice, managers can choose the risk level of their firms as well as take actions to change it, but the standard agency model tends to ignore this perspective. Our model is subject to the same criticism. 7 This assumption is innocuous as, in the real world, managers are subject to many rules and restrictions to trade stocks, particularly stocks of the companies under their management. 8 We use the firm s gross proceeds instead of the net proceeds in the pricing function to obtain analytically tractable solutions. Because in our model W is linear in both P and r, factoring W in the pricing function does not change the information content of the stock price. The stock price derived from this pricing function is informationally equivalent to the price derived from the more general pricing function specification, P = E r W (see also Baiman and Verrecchia 1995, Milbourn 2003). At time 1, the payoff is realized, the incentive contract is honored, and the firm is liquidated. The resulting liquidation proceeds are distributed between the manager and the principal. All players but the manager are risk neutral. The manager s preference is represented by a negative exponential utility function over her compensation W with the (absolute) risk-aversion coefficient. Her cost of choosing the effort e is denoted as C e = 1 2 ke2. The cost is measured in money and is independent of the manager s wealth. Given her choice of effort e, the manager s evaluation of the normally distributed income W can be represented in the certainty equivalent measure as follows: U W e = E W Var W C e (2) Equilibrium We solve a rational-expectation equilibrium in which the players in the real sector, i.e., the principal and the manager, use the information contained in the stock price and the realized payoff to make decisions, and both the real sector and the stock market attain equilibrium. We first solve the stock market equilibrium. The market maker sets a linear price schedule of the form P = e + (Kyle 1985). Using standard techniques, we obtain the equilibrium value of as = Vz 1/2 1/2, where = NV 2 V + V / N + 1 V + 2V 2. The expected profit of an informed trader is given by ER = V V + V 1/2 Vz 1/2 / N 1/2 N + 1 V + 2V. A potential trader searches for the private signal if and only if the expected profit from doing so exceeds her reservation value. The equilibrium number of informed traders N is determined by V V + V 1/2 Vz 1/2 = (3) N 1/2 N + 1 V + 2V We then analyze the incentive contract. Following Holmstrom and Tirole (1993), we transform the wage function into the following equivalent normalized form: W = â + bp + f ˆr (4)

5 686 Management Science 56(4), pp , 2010 INFORMS where â = a + fe, ˆr = r e, and e is the equilibrium effort level. Note that Equation (4) is just a reparametrization of Equation (1) at the hypothesized equilibrium value. The contracting analysis becomes much easier analytically with the normalized wage equation, so we build our analysis on this transformed compensation function from this point onward. One way to interpret Equation (4) is that besides the stock price P, the principal observes another signal, ˆr, and includes the signal into the compensation contract. The zero-mean ˆr can be understood as a signal on the firm s reported earnings, on which the principal also relies to better detect the managerial effort. 9 Using the standard agency-theory approach, we have the following: Lemma 1. In the rational-expectations equilibrium, the compensation contract can be rewritten as ( ) Cov P W = â + b P ˆr (5) Var with f = b Cov P /Var. The equilibrium payperformance sensitivity b is given by b = kvar P 1 2 (6) where Corr P. The equilibrium effort level e is given by e = b k (7) In equilibrium, f is negative because is positive (see Lemma 3). The intuition is similar to the relative performance argument in Holmstrom and Milgrom (1987). By construction, ˆr acts as one signal, in addition to the stock price P, to help the principal better extract the information about the managerial effort. If ˆr is high, then the principal knows that the exogenous shock is positive, and hence will lower the agent s compensation. In a different framework to analyze the use of reported accounting earnings and stock price as basis for managerial compensation, Baiman and Verrecchia (1995) obtain a similar result: The negative weight on reported earnings signal in the manager s contract is used to imperfectly extract the manager s actual effort from the stock price. Define x P Cov P /Var ˆr. We can view x as an aggregate performance index built on two performance measures, P and ˆr. The compensation scheme in our model is hence based on an aggregate measure that captures various aspects of a firm s performance Properties ofequilibrium Lemma 2. The number of informed traders, N, increases as the uncertainty of the firm s cash flow, V, increases. The intuition behind Lemma 2 is as follows. Each potential informed trader engages in a strategic activity in this environment. Given the other potential traders actions, her expected profit ER from collecting the costly private signal and becoming an informed trader increases as the uncertainty of the firm s cash flow V increases, which can been easily shown because ( ER/ V N =n > 0. Other potential outsiders will follow the same strategy and choose to become informed. Thus, the equilibrium number of informed traders increases as the firm s risk, measured by the firm s cash flow variance V, increases. Lemma 3. The correlation coefficient is positive. Moreover, both 2 and Var P are increasing functions of the underlying uncertainty V. Lemmas 1 3 imply that as the underlying uncertainty V increases, two opposing effects arise: (1) an outright decrease in managerial incentives, and (2) improved incentives caused by increased information-based trading. The overall effect thus depends on which effect dominates in equilibrium. Proposition 1. Define Var MP Var P 1 2. The overall response of the optimal pay-performance sensitivity b to the change in the fundamental uncertainty V is given by where with db k d Var MP = (8) dv 1 + kvar MP 2 dv PC = Var MP V d Var MP dv = PC IE (9) = N N + 1 V 3 + 6NV2 V + 8NV V 2 N + 1 V + 2V 3 > 0 (10) 9 To interpret r as a reliable signal on reported accounting earnings, we have to assume that the manager truthfully reports earnings. Factoring the manager s incentives to misreport earnings only makes ˆr noisier but does not change our results qualitatively because, by construction, ˆr plays only the role of a signal. 10 Executive compensation contracts in the real world are often written on a variety of performance measures such as economics value added, return on invested capital, total returns to shareholders, etc. The aggregate measure we propose in Equation (5) thus reflects the features of the incentive pay scheme in the real world.

6 Management Science 56(4), pp , 2010 INFORMS 687 and IE = Var MP N dn dv = V 2 V + 2V N 1 V 2V N + 1 V + 2V 3 dn (11) dv where IE > 0 if N > V + 2V /V. Moreover, the PC term strictly dominates the IE term, and d Var MP /dv > 0. Proposition 1 shows that two offsetting effects arise out of a growing uncertainty. The PC term measures the direct effect of an increase in uncertainty on incentives for a fixed number of informed traders. In sharp contrast, the IE term reflects the effect of an increasing amount of information-based stock trading resulting from a greater uncertainty. As the uncertainty rises, more potential traders collect information and trade on the information (Lemma 2). Through trading, more information will be incorporated into the stock price, and the correlation between the stock price and the cash flow increases (Lemma 3). The IE term thus characterizes the effect of the information-based trading on incentives. Combining Proposition 1 with Lemma 1, we obtain the following: Proposition 2. As the cash flow uncertainty increases, both the equilibrium pay-performance sensitivity and the equilibrium effort level decrease. The magnitude of the decrease is smaller for firms with a high level of information-based stock trading (or a high IE effect) than for firms with a low level of information-based stock trading (or a low IE effect). Proposition 2 implies a negative risk incentive relation, even after taking into account the IE effect. Note that IE equals zero if N is a constant (i.e., no riskdriven information-based trading). When IE is zero, the PC term alone, measuring the traditional risk incentive trade-off, captures the overall risk incentive relation. In the presence of information-based stock trading, the IE effect, due to a greater uncertainty, offsets the negative risk incentive relation. 3. Numerical Analysis We use real-world stock market data and executive compensation data to calibrate key parameters of the model. We then use the calibrated parameters to gauge the economic significance of the informationbased stock trading via a welfare analysis Calibration: Baseline Values Exogenous parameters in this model consist of the absolute risk-aversion coefficient, the parameter on manager s disutility of effort k, the cash flow variance V, the signal noise variance V, the liquidity order variance V z, and the reservation utility of becoming an informed trader. We normalize V, V z, and by the scale of V and define stn V /V, ztn V z /V and smu /V, respectively. We calibrate the parameters of our model based on a data set merging the Center for Research in Security Prices, Compustat, ExecuComp, and Thomson Financial s Institutional Holding databases over the period from 1992 to All monetary variables are in units of one million 2005 constant dollars. Baseline values for the parameters and relevant variables are denoted by a subscript 0, and their values are reported in panel B of Table 1. In our model, e and V are the mean and variance of a firm s payoff, respectively. Measuring the payoff by the firm s market value, we set e to the sample mean of the firm market value, i.e., e = Because our data cover a wide range of firms, from firms with very small market value ($8.49e 3 million) to firms with very large market value ($594, million), the pooled cross-sectional variance of firm market values is not a valid measure of the uncertainty about firm value. We use the cross-sectional average of the time-series variance of each individual firm market values, resulting in V 0 = We use the trading volume of a firm s common shares during a calendar year as a proxy for the total order flow. The trading volume also displays large cross-sectional variation, ranging from 0 to 27, million shares. Therefore, we calculate the volatility in trading volume as the timeseries standard deviation in trading volume for each firm over the sample period. The cross-sectional average of the standard deviations in the trading volume is (million shares), so we set the variance of the total order flow V = = Moreover, it is well accepted in the literature that institutional investors are informed traders, so we set the number of informed traders N to the average number of institutional investors for our sample firms, which is Finally, we follow the literature to choose values of the risk-aversion coefficient ; we set 0 = 2 (e.g., Haubrich 1994) There are different types of informed traders other than institutional investors in the market, such as corporate insiders, equity analysts, hedge funds, etc. Our choice for the number of informed traders may underestimate and provide a lower bound for the number of informed traders. In unreported analysis, we also pick higher values for the number, and the ensuing calibration yields qualitatively similar results. Moreover, we conduct various sensitivity analyses by choosing different values for the other parameters. All those results are qualitatively similar and are available upon request. 12 There is a typo in Haubrich (1994, p. 274), where is said to equal four. However, based on the assumed values for the other parameters and the implied pay-performance sensitivity of , it can only be the case that = 2.

7 688 Management Science 56(4), pp , 2010 INFORMS Table 1 Summary Statistics of Data and Baseline Values of Calibrated Parameters and Variables Panel A: Relevant summary statistics of data Variables Mean Std. dev. Median Min Max Firm value ($M) e Uncertainty in firm value ($M) Trading volume (M shares) Volatility in volume e (M shares) Number of institutional investors Incentives (PPS) Parameters and variables Panel B: Baseline values Calibrated values Chosen values e E r 6, V 0 Var r V N Calibrated values b k e 6 stn 0 V V smu 0 V e 5 ztn 0 V z V e 4 Notes. We calibrate our model s parameters based on a sample that is formed from merging the CRSP, Compustat, ExecuComp, and Thomson Financial s Institutional Holding databases over the period from 1992 to 2005, containing 2,692 firms and 24,577 firm-year observations. Panel A presents summary statistics of the data relevant to the calibration analysis. We obtain the firm value (in millions of 2005 constant dollars) as the product of fiscal yearend stock price and the total number of shares outstanding. We measure the uncertainty in firm value for a given year by a firm s standard deviation of shareholder dollar returns, which we compute as the annualized percentage standard deviation of the past five-year monthly stock returns multiplied by the beginning-of-year firm value (in millions of 2005 constant dollars). We obtain trading volume (in millions of shares) for a fiscal year as the volume of a firm s common shares traded within a calendar year corresponding to the fiscal year, and we calculate the volatility in trading volume as the time-series standard deviation in trading volume for the firm over the sample period. We obtain the number of institutional investors from the Thomson Financial s Institutional Holding database. We measure incentives by a CEO s direct ownership of stocks and stock options. Panel B reports the baseline values of calibrated parameters and variables. Using a multistep, internally consistent approach (see Appendix B), we achieve convergence in calibration when we set b 0 = 0 042, representing a $42 annual increase in a CEO s firm-related wealth (including options and stocks) per $1,000 increase in the shareholder wealth (Jensen and Murphy 1990). This value is close to our sample mean (panel A of Table 1; see also Table 1 of Aggarwal and Samwick 2003) as well as the OLS estimates of the pay-performance sensitivity (PPS) in the literature (see, e.g., Aggarwal and Samwick 1999, Murphy 1999). The parameter on the manager s disutility of effort, k 0, is calibrated to be e 6. As a result, the manager s disutility of choosing the effort is C e = 1 2 ke2 = units in certainty equivalent measure, which is 2.10% of the average market value of firms. Given the binding individual rationality condition at equilibrium and normalizing the manager s reservation utility to zero, we infer that the average compensation of the manager is no smaller than her disutility of choosing the effort (see Equation (A1) in Appendix A). This calibration result further indicates that the executive compensation accounts for at least 2.10% of the average market value of firms. To put this value in perspective, Bebchuk and Grinstein (2005) report that topexecutive compensation amounted to approximately 5% of the companies net income for the period, and the ratio rose to 9.8% in the period. The ratio stn 0, which measures the relative importance of the noise term in the informed trader s signal, equals This ratio suggests that approximately 1.81% of the variation in stock returns is predictable at the one-year horizon, which is consistent with empirical findings from the stock market return predictability literature. We obtain the ratio ztn 0 = e 4, and in turn, we calculate the variance of liquidity orders V z = , implying that 20.19% of the variation in total orders is due to the liquidity orders. Finally, the ratio of the reservation value of being an informed trader to the underlying cash flow variance, smu 0, is e 5, implying that the reservation value to become an informed trader is units. Because the reservation value and the profit of informed trading are equal in equilibrium, we infer that the profit of informed trading is also units, which is translated into approximately 4.18% of the average market value of firms Welfare Analysis Our model sheds light on the connection between the stock market efficiency and the economic efficiency. We view the stock market efficiency in terms of information production in the stock market, and the economic efficiency in terms of social welfare improvement. Dow and Gorton (1997) show that the stock market helps improve economic efficiency by providing more information to guide investment decisions. We focus on the stock market s role in structuring managerial incentives. We conduct the following numerical analysis to illustrate the economic significance of this information production channel. In our model, the information-based trading determines the amount of the information content in stock prices. We conduct a comparative static analysis by

8 Management Science 56(4), pp , 2010 INFORMS 689 allowing the underlying uncertainty V to increase from the baseline value up to by 200% with an increment of 1%. Fixing the other parameters at the above-calibrated baseline values and for each uncertainty level, we calculate the equilibrium number of informed traders N from Equation (3). Consistent with Lemma 2, N increases monotonically, from the initial level of 164 to 197 when V doubles and further to 209 when V triples. As Proposition 1 predicts, both PC and IE are positive and IE is smaller than PC (IE is positive because N>1 + 2stn 0 = 109 in this exercise). The ratio of IE over PC rises monotonically from the initial level of 9.18% to 22.78% when V doubles, and this ratio climbs further to 27.95% when V triples. Moreover, the gap between the two effects narrows as the underling uncertainty mounts, indicating an increasingly stronger offset of the IE effect relative to the PC effect. At equilibrium, the manager s ex ante utility is fixed at U a = U a, and the principal s ex ante utility is U p = E r W = b/k b 2 /2 Var P f 2 /2 Var bf Cov P b 2 / 2k U a. (See the proof of Lemma 1 in Appendix A.) The social welfare is the sum of the principal s ex ante utility and the manager s ex ante utility: 13 SW = b k b2 2 Var P f 2 b2 Var bf Cov P 2 2k = b k b2 2 Var P 1 2 b2 2k (12) For the welfare analysis, we examine the following two scenarios: 1. N = n 0, where n 0 is the initial equilibrium number of informed traders in the stock market. This corresponds to the case where the stock market produces information but the amount of produced information is fixed. This situation may also resemble the case where some legal or institutional rules are in place to prohibit any potential trader from becoming an informed trader except the n 0 existing informed traders. 2. N changes according to Equation (3) as the cash flow uncertainty changes, which corresponds to the case where a greater uncertainty attracts more information-based stock trading. Let SW 1 and SW 2 represent the levels of social welfare in Scenarios 1 and 2, respectively. We calculate SW 1 and SW 2 using the baseline values of the 13 Because informed traders, liquidity traders, and market makers are all risk neutral and the stock market is a zero-sum game in this economy, i.e., the profit of the informed trader equals the loss of the liquidity traders and the market makers break even ex ante, the net welfare of the stock market is zero. Thus, the SW term defined in Equation (12) is the social welfare for the entire economy including both the real and financial sectors. Figure 2 Responses of Social Welfare to Changes in Uncertainty V : Baseline Values Social welfare Percentage offset in social welfare reduction 3,200 3,000 2,800 2,600 2,400 2,200 2,000 1,800 1, Percentage increase in uncertainty Panel A: Responses of SW to percentage increases in V Panel B: Percentage offsets of the risk-welfare trade-off due to information enhancement Percentage increase in uncertainty Notes. Panel A plots different levels of social welfare in response to percentage changes in the underlying uncertainty V. The dashed line (SW 1 ) and the solid line (SW 2 ) represent the social welfare responses for the cases N = n 0, and N changes according to Equation (3), respectively. Panel B plots the percentage offsets of the social welfare reduction against percentage increases in uncertainty V. We compute the difference between the decline in SW 2 and the decline in SW 1 as a result of the increases in V, and then divide the difference by the magnitude of the decline in SW 1 to obtain the percentage offset of the risk welfare trade-off. parameters in Table 1. Figure 2, panel A graphs the two social welfare levels against percentage increases in the underlying uncertainty. The dashed and solid lines stand for SW 1 and SW 2, respectively. Both SW 1 and SW 2 are strictly downward sloped, indicative of a trade-off between the social welfare and uncertainty for a given level of information production. The information enhancement effect is strictly dominated (Proposition 2), leading to an overall risk incentive trade-off as well as a negative risk welfare relation. Strictly dominated as it is, the information

9 690 Management Science 56(4), pp , 2010 INFORMS enhancement effect contributes to a significant welfare improvement. In the figure, the SW 2 curve tops the SW 1 curve, and the gap widens as the uncertainty mounts. Starting from the same initial level, SW 2 exceeds SW 1 by 9.80% when V doubles, and by 17.14% when V triples. To measure the social welfare improvement due to the information enhancement, we compute the difference between the decline in SW 2 and the decline in SW 1 as a result of the increases in V, and then divide the difference by the magnitude of the decline in SW 1 to obtain the percentage offset of the risk welfare trade-off. Figure 2, panel B plots the percentage offsets of the social welfare reduction against percentage increases in uncertainty V. The offset gains in strength as the underlying uncertainty builds up. When V rises by 1% from the initial value, the offset is 9.38%. The offsets reach 17.96% and 20.29% when V doubles and triples, respectively. 4. Empirical Analysis To offer more direct evidence, in this section, we empirically study the impact of information-based stock trading on CEO incentives and the risk incentive relation Data and Variables Data for this empirical study are from several sources. CEO compensation data come from the ExecuComp database and data on stock returns and accounting information are from the CRSP Monthly Stock File and the Compustat Annual File, respectively; we obtain from Jefferson Duarte the data of probability of informed trading (PIN), which is constructed from intraday trading data of the Trade and Quote database; we extract institutional ownership information from the Thomson Financial s Institutional Holding database. Because of the availability of data to construct various variables used in our empirical analysis, the final sample spans the period from 1992 to 2005 and consists of 11,795 firm-year observations except for the directly constructed incentive measure PPS, which has 10,166 observations. We measure CEO incentives using Jensen and Murphy s (1990) pay-performance sensitivity, which is the dollar value change in CEO s firm-specific wealth per $1,000 change in shareholder value. There are two popular ways to construct this incentive measure. One way is to estimate pay-performance sensitivities from a regression of CEO compensation on firm performance (e.g., Jensen and Murphy 1990, Aggarwal and Samwick 1999, Milbourn 2003), and we defer to 4.2 for the detailed discussions of this regression (i.e., Equation (14)). We calculate the change in CEO s firm-specific wealth (COMP), in thousands of dollars, as the sum of total direct flow compensation, value realized from exercising options, and changes in value of CEO holdings of options and stocks. The ExecuComp database reports total direct flow compensation, which is the sum of salary, bonus, Black-Scholes value of stock option grants, restricted stock grants, long-term incentive plan payouts, and other annual compensation; the change in value of stock holdings is computed as the beginning-of-year value of CEO s stock holdings multiplied by the current year s inflation-adjusted annual stock return (ANNRET); the change in value of stock options equals the product of option deltas, calculated using Core and Guay s (1999) method, and the change in the firm s market value after adjusting for the share percentage represented by existing stock options. To obtain the change in a firm s shareholder value (VCHGE) for a given year, we first obtain the firm value (MKTVAL), in million dollars, as the product of fiscal year-end stock price and the total number of shares outstanding, and we then calculate VCHGE as that year s inflation-adjusted annual stock return (ANNRET) multiplied by the beginning-of-year firm value. Thus, VCHGE is the dollar return to shareholders and measures the firm s performance. Table 2 summarizes those variables. The sample covers a wide range of firms with market capitalization ranging from $1.67 million to more than $594 billion. As a result, the change in shareholder value, VCHGE, also exhibits a large variation. This table also shows the existence of extreme outliers in the CEO compensation data. The minimum and maximum values of COMP are, respectively, a loss of more than $7.24 billion and a gain of $14 billion, both due to the change in the value of stock-based compensation. Another popular way to construct the measure of pay-performance sensitivity directly uses executives ownership of stocks and stock options (e.g., Core and Guay 1999, Jin 2002, Aggarwal and Samwick 2003), because the stock-based incentives are well documented to simply swamp the incentives from other compensation components and constitute the overwhelming heterogeneity in the empirically estimated pay-performance sensitivity (e.g., Hall and Liebman 1998 and Murphy 1999). We calculate the stock-based pay-performance sensitivity PPS as the fraction of the firm the CEO owns, plus the fraction of the firm s stocks on which the options are written, times the options deltas, and multiplied by 1,000. Table 2 shows summary statistics of this alternative incentive measure, which has a mean of , a median of 7.539, and a standard deviation of Firm risk and the amount of information-based stock trading are two key variables for our empirical analysis. Following Aggarwal and Samwick (1999) and Jin (2002), we measure a firm s risk by the dollar return standard deviation, STDV. We compute STDV

10 Management Science 56(4), pp , 2010 INFORMS 691 Table 2 Summary Statistics of Data for Regression Analysis Variables Mean Std. dev. Median Min 1% 25% 75% 99% Max 1 1 MKTVAL ($M) SIZE ($M) ANNRET ANNVOL VCHGE ($M) STDV ($M) PIN PINF PINR 1.67e e TOTHLD e CON TOBIN INV LEV KZ COMP ($K) e e+7 TENURE LNTEN PPS Notes. We obtain the firm value (MKTVAL, in millions of dollars) as the product of fiscal year-end stock price and the total number of shares outstanding. We denote by SIZE the logarithm value of firm value. We calculate the change of firm value (VCHGE) in a given year as that year s inflation-adjusted annual stock returns (ANNRET) multiplied by the beginning-of-year firm value (in millions of dollars). We measure risk by a firm s standard deviation of shareholder dollar returns (STDV), and we compute STDV of a given year as the annualized standard deviation of the past five-year inflation-adjusted monthly stock returns (ANNVOL) multiplied by the beginning-of-year firm value (in millions of dollars). We use Duarte and Young s (2009) adjusted probability of informed trading (PIN) measure, which is developed from an extended version of the Easley et al. (1996) structural microstructural model, to measure the amount of information-based stock trading. The two variables, PINF and PINR, are separately the fitted values and residuals from year-by-year cross-sectional regressions of PIN against SIZE and STDV (see Table 3 for details). We calculate aggregate institutional holding (TOTHLD) as the total institutional share holdings scaled by the total number of shares outstanding. We compute the concentrated ownership (CON5) as the top-five institutional share holdings in proportion of the total institutional share holdings. We calculate Tobin s Q (TOBIN) as the ratio of the market value of assets to the book value of assets, where the market value of assets is defined as the book value of assets (data 6) plus the market value of common equity (data 25 times data 199) less the book value of common equity (data 60) and balance sheet deferred taxes (data 74). We compute the investment-to-capital ratio (INV) as capital expenditure (data 128) divided by fixed assets (data 8), and the leverage ratio (LEV) as the sum of short-term debt (data 34) and long-term debt (data 9) divided by the sum of short-term and long-term debt and stockholders equity (data 216). We follow Kaplan and Zingales (1997) to calculate the KZ index (KZ) as a measure of financial constraint. We calculate the CEO total compensation (COMP), in thousands of dollars, as the sum of total direct flow compensation, value realized from exercising options, and changes in value of CEO holdings of options and stocks. The change in value of stock holdings is computed as the beginning-of-year value of CEO s stock holdings multiplied by the current year s inflation-adjusted stock return; the change in value of stock options equals the product of option deltas, calculated using Core and Guay s (1999) method, and the change in the firm s market value after adjusting for the share percentage represented by existing stock options. We compute TENURE as a CEO s tenure as of year t, and LNTEN as the logarithm value of the CEO s tenure. The stock-based pay-performance sensitivity (PPS) represents incentives provided by the CEO s direct ownership of stocks and stock options, which is the fraction of the firm the CEO owns plus the fraction of the firm s stocks on which the options are written times the options deltas, multiplied by 1,000. All monetary variables are quoted in 2005 constant dollars. The sample spans the period from 1993 to 2005 and contains 11,795 firm-year observations without missing values in any of the listed variables except PPS, which has 10,166 observations. in a given year as the annualized standard deviation in the past five-year inflation-adjusted monthly stock returns (ANN VOL) multiplied by the beginning-ofyear firm value. As pointed out in Aggarwal and Samwick (1999), this measure accounts for the property that larger (smaller) firms tend to have larger (smaller) variance by virtue of scale. To measure the amount of information-based stock trading, we use probability of informed trading (PIN), developed from a structural microstructural model in Easley et al. (1996), which reflects how the mechanics of a trading process affect the information content of a stock price. By extending the original sequential trade model, Duarte and Young (2009) decompose PIN into two components, one related to asymmetric information and the other to illiquidity. We thus use Duarte and Young s adjusted PIN measure that is related to asymmetric information, denoted by PIN, as the proxy for the amount of information-based stock trading. 14 Table 2 presents summary statistics of the two key variables. Notably, STDV is severely skewed to the right. We also construct a set of firm-specific and CEO-specific control variables, which are known to correlate with heterogeneity in pay-performance sensitivities. To control for institutional influence, we 14 We thank one referee for suggesting the use of the adjusted PIN measure. Note that our paper is not about whether and which component of PIN is priced in cross-section. In fact, Duarte and Young (2009) show that liquidity effects unrelated to information asymmetry explain the relation between PIN and the cross-section of expected returns as documented in Easley et al. (2002).

11 692 Management Science 56(4), pp , 2010 INFORMS define TOTHLD as the total institutional share holdings in proportion of the total number of shares outstanding, and CON5 as the proportion of total institutional share holdings by the top five institutional investors in the firm. To measure a firm s growth opportunity, we calculate Tobin s Q (TOBIN) as the ratio of the market value of assets to the book value of assets. We obtain the market value of assets as the book value of assets (data 6) plus the market value of common equity (data 25 times data 199) less the book value of common equity (data 60) and balance sheet deferred taxes (data 74). To capture the effects of a firm s investment policy and capital structure on CEO incentives, we compute the investmentto-capital ratio (INV) as capital expenditure (data 128) divided by fixed assets (data 8), and the leverage ratio (LEV) as the sum of short-term debt (data 34) and long-term debt (data 9) divided by the sum of shortterm and long-term debt and stockholders equity (data 216). Furthermore, to characterize the impact of a firm s financial constraints on CEO incentives, we follow Kaplan and Zingales (1997) to construct the KZ index (KZ). Other control variables include CEO tenure (TENURE), and dummies for each year and each industry (Dummies). To capture the potential nonlinear relation between CEO incentives and CEO tenure, we use the logged value of the CEO s tenure (LNTEN) in our empirical analysis. Table 2 summarizes these control variables, except Dummies Hypothesis and Econometric Strategy Our model predicts that two effects arise in response to an increase in the fundamental uncertainty. Apart from directly reducing incentives, a rise in uncertainty (or risk) encourages information-based trading in the stock market, which increases the information content of the stock price and, in turn, improves incentives Decomposition ofpin. As shown in our model, the amount of information-based trading is not merely related to risk. Other factors such as liquidity, noisiness of private signals, and the reservation value of becoming informed traders also affect the information-based trading and consequently CEO incentives. The empirical measure of informationbased stock trading, PIN, may contain components that help improve CEO incentives but are unrelated to risk. To address this concern, we separate PIN into two components, one related to risk and the other not, by running the following cross-sectional regression on a yearly basis: 15 PIN it = c 0 + c 1 SIZE it + c 2 STDV it + e it (13) 15 In an earlier draft, we include the squared STDV instead of SIZE in the regressions to capture the potentially nonlinear relation between PIN and STDV. We retain this exercise in the current draft and the results are similar. For brevity, those results are not reported and are available upon request. where SIZE is the logarithm value of a firm s market capitalization. We use the fitted values (PINF) and the residuals (PINR) of the year-by-year crosssectional regressions to measure the two components of PIN that are related and unrelated to risk, respectively. This PIN decomposition model deserves a further discussion. Besides the dollar return risk measure STDV, we include firm size in the decomposition regressions for two reasons. First, because our risk measure STDV is mechanically and positively correlated with firm size, which is well known to significantly and negatively correlate with PIN (Easley et al. 2002), a univariate regression of PIN on STDV yields a significantly negative coefficient estimate on STDV. The negative loading of PIN on STDV in the univariate regression appears to be dominated by and pick up only the impact of firm size on PIN even though PIN is positively and significantly correlated with the percentage return risk measure ANNVOL. 16 Therefore, we believe that in the bivariate regression like Equation (13), the coefficient estimate on STDV correctly captures the impact of risk on informationbased trading after controlling for the (unwanted) role of firm size. Second, the current specification allows us to better gauge the economic significance of change in firm risk on information-based trading as well as incentive provision. Note that the fitted value PINF from Equation (13) includes the firm size element, which is well known to be negatively related to payperformance sensitivities (e.g., Schaefer 1998). As a result, our estimation using this PINF measure may underestimate the impact of information-based stock trading on incentive improvement. Table 3 reports the regression results of Equation (13) for each year over the period. It is clear that, consistent with the literature, PIN is inversely related to firm size (Easley et al. 2002) the coefficient on SIZE is negative each year. The table also shows that PIN is positively correlated with firm risk after controlling for firm size: The coefficient on STDV is positive for almost all years except The adjusted R 2 s of the decomposition regression average at over the sample period and show an increasing trend, jumping from below 0.40 in the 1990s to over 0.60 after Econometric Models. Using the two PIN components, we follow Jensen and Murphy (1990) 16 In fact, if we run a bivariate regression of PIN on SIZE and ANNVOL, the coefficients estimates on SIZE and ANNVOL are significantly negative and significantly positive, respectively.

12 Management Science 56(4), pp , 2010 INFORMS 693 Table 3 PIN Decompositions PINF PINR Year Intercept SIZE STDV Adj. R 2 No. of obs. Mean Median Std. dev. Mean Median Std. dev e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e Average e Notes. This table reports the results of annual cross-sectional regressions to decompose the proxy for the amount of information-based stock trading, PIN, against firm size, SIZE, and firm risk, STDV. The variables are defined as in Table 2. The regressions are estimated year-by-year over the period from 1992 to 2004, and we denote by PINF and PINR the fitted values and the residuals of the regressions, respectively. The last row reports the average values of each estimate across the period. and Aggarwal and Samwick (1999) to specify our main econometric model as follows: COMP i t = 0 +VCHGE i t ( STDV i t + 2 PINF i t PINR i t 1 + k 4 ) k Controls + 1 STDV i t + 2 PINF i t PINR i t 1 + k 4 k Controls+ i t (14) In this specification, PINF and PINR represent, respectively, the information-based stock trading related and unrelated to firm risk; Controls includes the set of control variables such as TOTHLD t 1, CON5 t 1, TOBIN t 1, KZ t 1, LEV t 1, INV t 1, LNTEN t, year dummies, and industry dummies. Equation (14) implies that we can calculate the payperformance sensitivity (PPS) as PPS i t = STDV i t + 2 PINF i t PINR i t 1 + k 4 k Controls (15) where the coefficient 1 reflects the direct effect of firm risk on CEO incentives and is expected to be negative. The coefficient 2 captures the effect of risk-related information-based trading on CEO incentives, which we interpret as an indication of the indirect effect of risk on CEO incentives through information-based stock trading. This coefficient is the parameter of interest and is expected to be positive based on our model prediction. The coefficient 3 characterizes the effect on CEO incentives of the information-based trading not accounted for by risk, and we do not have a clear prediction about its sign. Here, a significantly positive 2 and a significantly negative 1 suggest the offset against risk incentive trade-off driven by the risk-related component of information-based stock trading. Thus, the overall risk incentive relation based on Equation (14) is equal to PINF/ STDV. Accordingly, the size of the offset is measured as the absolute value of ( 2 PINF/ STDV / 1. Table 2 shows clear evidence on the presence of extreme outliers in the data, particularly on CEO compensation COMP, firm risk STDV, and payperformance sensitivity PPS. Consequently, we winsorize each of the three variables at the 1st and 99th percentiles. To further reduce the impact of outliers on estimations, we follow Aggarwal and Samwick (1999) and estimate Equation (14) with median regressions because the method is less susceptible to large outliers than other estimators. We compute the standard errors of parameter estimates with 20 bootstrap replications. To check robustness, we further estimate Equation (14) with fixed-effect OLS regressions. In the OLS regression, we include the CEO-firm fixed effects to control for all differences in the average level of CEO compensation; we calculate heteroscedasticityrobust standard errors and adjust for clustering at the firm level. Also, we adopt another commonly used approach in the executive compensation literature to regress the directly constructed pay-performance sensitivity PPS against variables of interest and control variables (e.g., Core and Guay 1999, Jin 2002).

13 694 Management Science 56(4), pp , 2010 INFORMS Consequently, we estimate Equation (15) with both median regressions and CEO-firm fixed-effect OLS regressions Empirical Results Table 4 presents the estimation results for the two models, with columns 1 and 2 corresponding to Equation (14) and columns 3 and 4 to Equation (15). We start with the median regression results for Equation (14). The coefficient estimate on the firm risk STDV is negative and significant at the 1% level, consistent with the standard agency theory. The coefficient estimate on PINF is positive and significant at the 1% level, indicating that the risk-related information-based trading is associated with a higher level of CEO incentives. The coefficient on PINR is positive and significant at the 1% level, suggesting that the non-risk-related component of informationbased stock trading improves CEO incentives as well. The median regression results also show that CEO incentives are positively related to aggregate and concentrated institutional holdings, growth opportunities, investment expenditure, and CEO tenure, and are negatively related to financial constraints and leverage ratio. These results are largely in line with the findings in the literature. The two parameters of interest are the coefficients on STDV and PINF because the overall risk incentive relation is equal to PINF/ STDV. Table 3 reports that the average loading of PINF on STDV is 9.39e 7, that is, PINF/ STDV = 9 39e 7. Given a negative coefficient estimate on STDV and a positive coefficient estimate on PINF in our main econometric model, we can infer that there are two effects of firm risk on CEO incentives. The increase in firm risk directly reduces CEO incentives, as captured by the coefficient 1, and the increase in firm risk also indirectly enhances CEO incentives, which is characterized by the coefficient 2. The magnitude of the offset effect is captured by ( 2 PINF/ STDV / 1 and is economically meaningful. Using the median regression estimates, a onestandard-deviation increase in STDV causes a direct reduction of CEO incentives by 8.87e = 0 591; meanwhile, this increase in STDV causes an indirect improvement in CEO incentives through information-based trading by = because the increase in STDV causes PINF to increase by 9.39e = The percentage of the offset is 0 475/0 591 = 80 30%. The two positive coefficient estimates affiliated with the two PIN components demonstrate that the information-based trading positively affects CEO incentives by increasing the level of incentives (the level effect) as well as by reducing the slope of risk incentive relation (the slope effect). The level effect is attributable mainly to the non-risk-related component of information-based trading, and the slope effect attributable to the risk-related component of information-based trading. The slope effect depicts the nontrivial impact of risk on incentives as well: Aside from directly reducing incentives, an increase in the fundamental uncertainty indirectly induces incentives and (partially) offsets the incentive reduction by encouraging informed trading in the market and improving the information content of the stock price. We also estimate Equation (14) using the OLS regression, in which we include an CEO-firm fixed effect, calculate heteroscedasticity-robust standard errors, and adjust for clustering at the firm level. The OLS regression results are similar to the median regression results. The estimated coefficients on STDV and PINF are, respectively, negative and positive and both are significant at the 1% level; the estimated coefficient on PINR is positive but nonsignificant. Using the OLS estimates, we compute the percentage of the offset of the risk incentive trade-off as 9 39e / 2 26e 4 = 43 29% as a onestandard-deviation increase in STDV causes a direct reduction of CEO incentives by 2 26e = and an indirect improvement in CEO incentives by = We proceed to examine the estimation results for Equation (15). The results are similar. For example, PPS is significantly and negatively related to firm risk STDV, supporting the risk-return trade-off predicted by the standard agency theory. PPS is significantly and positively correlated with both the risk-related informed trading and the risk-unrelated informed trading, indicating that the information-based trading helps improve CEO incentives. The offset effect implied from estimates of Equation (15) has a similar magnitude as well. Using the median regression estimates, a one-standard-deviation increase in STDV causes a direct reduction of CEO incentives by 3.82e = 2 545; this increase in STDV also causes an indirect improvement in CEO incentives via the information-based trading by = 1 354, resulting in an offset of 1 354/2 545 = 52 82%. Using the OLS estimates, a one-standard-deviation increase in STDV causes a direct reduction of CEO incentives by 3.76e = and an indirect improvement in CEO incentives by = 2 041, resulting in an offset of 2 041/2 505 = 80 89%. 5. Summary and Conclusions In this paper, we investigate the role of informationbased stock trading in affecting the risk incentive relation. We construct a parsimonious principal-agent

14 Management Science 56(4), pp , 2010 INFORMS 695 Table 4 Regression Results Model 1(dependent variable is COMP) Model 2 (dependent variable is PPS) Parameters Median regression OLS-FE regression Median regression OLS-FE regression Intercept VCHGE VCHGE STDV 8 87e e e e 5 VCHGE PINF VCHGE PINR VCHGE TOTHLD VCHGE CON VCHGE TOBIN VCHGE KZ e VCHGE LEV VCHGE INV VCHGE LNTEN VCHGE Dummies Yes Yes STDV e e e e 4 PINF PINR TOTHLD CON TOBIN KZ LEV e INV LNTEN Dummies Yes Yes Yes Yes Sample size 11,795 11,795 10,166 10,166 R 2 /pseudo R Notes. This table reports the estimation results of the following two models: ( COMP i t = 0 + VCHGE i t STDV i t + 2 PINF i t PINR i t 1 + ) k Controls k STDV i t + 2 PINF i t PINR i t 1 + k 4 k Controls + i t PPS i t = STDV i t + 2 PINF i t PINR i t 1 + k 4 k Controls + v i t Here, PINF and PINR are separately the fitted values and residuals from year-by-year cross-sectional regressions of the proxy for the amount of informationbased stock trading, PIN, against SIZE and STDV (see Table 3 for details). The control variables Controls include TOTHLD t 1, CON5 t 1, TOBIN t 1, KZ t 1, LEV t 1, INV t 1, and LNTEN t, all defined in Table 2, year dummies, and industry dummies. We estimate the two models with either median regressions or OLS CEO-firm fixed-effect regressions and report standard errors in parentheses. We calculate the standard errors in median regressions based on 20 bootstrap replications; and the heteroscedasticity-robust standard errors in OLS-FE regressions adjust for clustering at the firm level. We suppress coefficient estimates on year dummies and industry dummies for brevity. The sample period is ,, Statistical significance at the 10%, 5%, and 1% levels, respectively.

15 696 Management Science 56(4), pp , 2010 INFORMS model that combines information-based stock trading with optimal contracting. The information content in stock price is endogenously determined and depends only on trading characteristics. We analytically decompose the equilibrium impact of risk on incentives into two offsetting effects. The direct effect measures the standard risk incentive trade-off given a level of information-based trading; the indirect effect reflects incentive enhancement due to the risk-related information-based stock trading. This informationproduction channel has so far been largely overlooked in the incentive literature. Using real-world executive compensation data and stock market data, we calibrate the model parameters and the economic significance of the information enhancement effect. The calibrated values of the parameters key to both optimal contracting and stock trading processes are broadly consistent with empirical evidence and offer support to the agency theory. Our analytical and quantitative results uncover the role of information-based trading in affecting CEO incentives apart from directly reducing managerial incentives, a greater uncertainty increases the level of information-based trading and, consequently, enhances managerial incentives and offsets the risk incentive trade-off. The numerical analysis illustrates that the risk-related information-based trading offsets approximately 20% 30% of the risk incentive tradeoff and brings about significant welfare improvement as the underlying risk increases. We further empirically test the prediction of our model and obtain supportive results. Depending on model specifications and estimation methods, we find that the risk-related information-based trading can offset the risk incentive trade-off by 43% to 81%. Our study not only highlights the important and understudied role of the risk-related informationbased stock trading in strengthening executive incentives but also generates useful managerial implications. In particular, our findings suggest that incentive pay may still be useful in an uncertain environment if the underlying stock trading is informative enough. The principals (i.e., boards of directors) thus should make an effort to promote information-based trading and incorporate trading characteristics (e.g., liquidity, stock price informativeness, structure of investor base, changes in positions of key institutional investors, etc.) into the contracting process. Our results also imply that incentive pay may not work in an environment in which higher risk and lower stock market information production coexist. Acknowledgments The authors thank David Hsieh (the department editor), one associate editor, two anonymous referees, Chong-En Bai, Hongbin Cai, Sudipto Dasgupta, Hassan Naqvi, Wing Suen, Xianming Zhou, and seminar participants at Beijing University, University of Hong Kong, and Asian Finance Association Annual Meeting for helpful comments and suggestions. They also thank Jefferson Duarte for sharing his PIN data, developed in Duarte and Young (2009). An earlier draft was completed while Qiang Kang was affiliated with the University of Hong Kong, whose hospitality is gratefully acknowledged. The authors appreciate financial support from the University of Miami McLamore Award (Qiang Kang) and the University Grants Committee of the Hong Kong Special Administrative Region, China (Projects HKU 7472/06H and HKU H, Qiao Liu). All errors remain the authors responsibility. Appendix A. Proofs Proof of Lemma 1. We set up the principal s problem as follows: max a b f e E r W s.t. max E W e 2 Var W c e U a (A1) where U a is the reservation utility to the manager. Given the compensation contract W = â + bp + f ˆr (as specified in Equation (4)), the manager solves the following problem: max â + be b2 e 2 Var P f 2 2 Var bf Cov P ke2 2 (A2) The first-order condition yields b = ke (A3) We therefore have Equation (7). At equilibrium, the manager s individual rationality condition should be binding, which yields â = U a be + b2 2 Var P + f 2 2 Var + bf Cov P + ke2 2 (A4) With W = â+bp +f ˆr, the principal s problem can be rewritten as max â b f 1 b e â s.t. b = ke â = U a be + b2 2 Var P + f 2 2 Var + bf Cov P + ke2 2 Substitute b/k for e and Equation (A4) for â. The above problem is therefore simplified as b max b f k b2 2 Var P f 2 2 The first-order conditions yield Var bf Cov P b2 2k 1 k b Var P f Cov P b k = 0 (A5) (A6)

16 Management Science 56(4), pp , 2010 INFORMS 697 and f Var bcov P = 0 We immediately obtain from Equation (A7) (A7) Cov P f = b (A8) Var Plugging f = b Cov P /Var back into Equation (A6), we obtain 1 b = Q.E.D. (A9) 1 + kvar P 1 2 Proof of Lemma 2. Using the implicit function theorem, we have dn = N 1/2 V 2 V + V 1/2 Vz 1/2 + 4 N 1/2 V dv 3N + 1 V + 2V V = N N + 1 V 2 + 6V V + 4V 2 V V + V 3N + 1 V + 2V > 0 Q.E.D. Proof of Lemma 3. Because = N + N i=1 i + z, we obtain V = N + 1 V + 2V / V + V V z. Furthermore, with P = e +, we have Var P = 2 V = NV 2/ N + 1 V + 2V. From the stock market equilibrium, we have Cov P = Cov = N V = NV 2/ N + 1 V + 2V = Var P. Then, 2 Cov 2 P / Var P V = NV / N + 1 V + 2V. Thus, d 2 /dv = V V + 2V dn /dv + 2NV / N + 1 V + 2V 2 > 0 because dn /dv > 0 (see Lemma 2). We then conclude that Var P = 2 V, and clearly, dvar P /dv > 0asd 2 /dv > 0. Q.E.D. Proof of Proposition 1. Using the results from the proof of Lemma 3 and applying the total differentials, we immediately obtain d Var MP /dv d Var P 1 2 /dv = PC IE, where PC and IE are defined as in Equations (10) and (11), respectively. To show that d Var MP /dv > 0, we need to show that PC >IE. That is, or N N + 1 V 3 + 6NV2 V + 8NV V 2 >V 2 V + 2V N 1 V 2V dn dv LHS N N + 1 V 3 + 6NV2 V + 8NV V 2 V + V 3N + 1 V + 2V (A10) > RHS NV V + 2V N 1 V 2V N + 1 V 2 + 6V V + 4V 2 (A11) This holds as the coefficient of each term in LHS is larger than that of its corresponding term in RHS. Q.E.D. Appendix B. The Calibration Method Given the chosen values for the parameters and variables as reported in the upper half of panel B of Table 1, we adopt the following internal-consistent multistep approach to calibrate the values of the other parameters because they do not have good empirical estimates. Step 1. We choose one initial value of the payperformance sensitivity, b. From Equation (7) we calculate k = b/e given e. Step 2. Defining Var MP Var P 1 2, and using the proof of Lemma 3 (available in Appendix A), we derive that Var MP = NV2 V +2V N +1 V +2V = N 1+2stn 2 N +1 +2stn V (B1) 2 Combining Equation (6) with Equation (B1), we obtain 1/b 1 k = N 1 + 2stn V N stn 2 (B2) Given b,, k, N, and V, we solve for stn from Equation (B2). Step 3. Using = N + N i=1 i + z, we derive which yields ztn V z V = V = N + 1 V + 2V V + V V z (B3) V + V N + 1 V + 2V V V = We then obtain ztn. Step 4. We rewrite Equation (3) as 1 + stn V N stn V (B4) smu = 1 + stn 1/2 ztn 1/2 N 1/2 N stn (B5) from which we calculate smu. Step 5. Given these calibrated parameter values, we recalculate Var MP from Equation (B1), and then we calculate b from Equation (6). We use Step 5 to check for the convergence of the calibration. If the value of b calculated from Step 5 is significantly different from the chosen initial value b in Step 1, then we pick another initial value b and repeat Step 1 to Step 5 until the two values are close to each other (with a difference less than 1e 10). References Aggarwal, R. K., A. A. Samwick The other side of the tradeoff: The impact of risk on executive compensation. J. Political Econom. 107(1) Aggarwal, R. K., A. A. Samwick Why do managers diversify their firms? Agency reconsidered. J. Finance 58(1) Baiman, S., R. E. Verrecchia Earnings and price-based compensation contracts in the presence of discretionary trading and incomplete contracting. J. Accounting Econom. 20(1) Bebchuk, L., Y. Grinstein The growth of executive pay. Oxford Rev. Econom. Policy 21(2) Chen, Q., I. Goldstein, W. Jiang Price informativeness and investment sensitivity to stock price. Rev. Financial Stud. 20(3) Core, J., W. Guay The use of equity grants to manage optimal equity incentive levels. J. Accounting Econom. 28(2) Dittmann, I., E. Maug Lower salaries and no options? On the optimal structure of executive pay. J. Finance 62(1) Dow, J., G. Gorton Stock market efficiency and economic efficiency: Is there a connection? J. Finance 52(3) Dow, J., R. Rahi Informed trading, investment, and economic welfare. J. Bus. 76(3) Duarte, J., L. A. Young Why is PIN priced? J. Financial Econom. 91(2) Easley, D., S. Hvidkjaer, M. O Hara Is information risk a determinant of asset returns? J. Finance 57(5) Easley, D., N. Kiefer, M. O Hara, J. Paperman Liquidity, information, and infrequently traded stocks. J. Finance 51(4)

17 698 Management Science 56(4), pp , 2010 INFORMS Edmans, A Blockholder trading, market efficiency, and managerial myopia. J. Finance 64(6) Faure-Grimaud, A., D. Gromb Public trading and private incentives. Rev. Financial Stud. 17(4) Fishman, M., K. Hagerty Insider trading and the efficiency of stock prices. RAND J. Econom. 23(1) Garen, J. E Executive compensation and principal-agent theory. J. Political Econom. 102(6) Hall, B. J., T. A. Knox Underwater options and the dynamics of executive pay-to-performance sensitivities. J. Accounting Res. 42(2) Hall, B. J., J. B. Liebman Are CEOs really paid like bureaucrats? Quart. J. Econom. 113(3) Hall, B. J., K. J. Murphy Stock options for undiversified executives. J. Accounting Econom. 33(1) Hartzell, J. C., L. T. Starks Institutional investors and executive compensation. J. Finance 58(6) Haubrich, J. G Risk aversion, performance pay, and the principal-agent problem. J. Political Econom. 102(2) Holmstrom, B Moral hazard and observability. Bell J. Econom. 10(1) Holmstrom, B., P. R. Milgrom Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55(2) Holmstrom, B., J. Tirole Market liquidity and performance monitoring. J. Political Econom. 101(4) Ittner, C. D., R. A. Lambert, D. F. Larcker The structure and performance consequences of equity grants to employees of new economy firms. J. Accounting Econom. 34(1) Jensen, M. C., K. J. Murphy Performance pay and topmanagement incentives. J. Political Econom. 98(2) Jin, L CEO compensation, diversification, and incentives. J. Financial Econom. 66(1) Kang, Q., Q. Liu Stock trading, information production, and executive incentives. J. Corporate Finance 14(4) Kaplan, S., L. Zingales Do financing constraints explain why investment is correlated with cash flow? Quart. J. Econom. 112(1) Kyle, A. S Continuous auctions and insider trading. Econometrica 53(6) Kyle, A. S., J. L. Vila Noise trading and takeovers. RAND J. Econom. 22(1) Lambert, R. A., D. F. Larcker, R. E. Verrecchia Portfolio considerations in valuing executive compensation. J. Accounting Res. 29(1) Milbourn, T CEO reputation and stock-based compensation. J. Financial Econom. 68(2) Murphy, K. J Executive compensation. O. C. Ashenfelter, D. Card, eds. Handbook of Labor Economics, Vol. 3B. Elsevier Science, Amsterdam, Prendergast, C The tenuous trade-off of risk and incentives. J. Political Econom. 110(5) Raith, M Competition, risk and managerial incentives. Amer. Econom. Rev. 93(4) Schaefer, S The dependence of pay-performance sensitivity on the size of the firm. Rev. Econom. Statist. 80(3) Subrahmanyam, A., S. Titman The going-public decision and the development of financial markets. J. Finance 54(3)