Information-Based Stock Trading, Executive Incentives, and the

Principal-Agent Problem ∗

Qiang Kang †

University of Miami

Qiao Liu ‡

University of Hong Kong

This Draft: November 2009

AbstractWe 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.

JEL Classification: D80, G14, G30, J33

Keywords: Risk-incentive tradeoff, endogenous information-based trading, pay-performance

sensitivity, adjusted PIN, calibration

∗We 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. We also thank Jefferson Duarte for sharing with us his PIN data, developed in Duarte and Young (2009).

An earlier draft was completed while Kang was affiliated with University of Hong Kong, whose hospitality is gratefully

acknowledged. We appreciate financial supports from the University of Miami McLamore Award (Kang) and the

University Grants Committee of the Hong Kong Special Administrative Region, China (Projects HKU 7472/06H and

HKU 747107H, Liu). All errors remain our own responsibility.†Corresponding author. Mailing address: Finance Department, University of Miami, P.O. Box 248094, Coral

Gables, FL 33124-6552. Phone: (305)284-8286. Fax: (305)284-4800. E-mail: q.kang@miami.edu.‡Faculty of Business and Economics, University of Hong Kong. Phone: (852)2859-1059. Fax: (852)2548-1152.

E-mail:qliu@hku.hk.

1 Introduction

A standard principal-agent model predicts a negative relation between risk and incentives

(Holmstrom 1979; and 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 information-based stock trading in affecting executive

incentives. We propose that information-based stock trading 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 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 two-fold. 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 under-studied. 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

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.

1

from which boards can learn to better manage executive compensation.

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 tradeoff effect given certain amount of information-based trading, and

the other reflects the incentive enhancement effect due to the information-based 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 real-world executive compensation data and stock

market data we calibrate our model with an internally consistent multi-step approach. Our

calibration analysis demonstrates the following: (1) the pay-performance sensitivity equals 0.042,

representing a $42 increase in CEO compensation per $1000 increase in shareholder value; (2) the

manager’s disutility (in certainty equivalent measure) from effort equals about 2.10% of the average

market value; (3) the profit of informed trading is about 4.18% of the average market value; (4)

about 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 1992-

2005. We use Duarte and Young’s (2009) adjusted probability of informed trading (PIN), which

is developed from an extended version of the Easley, Kiefer, O’Hara, and Paperman (1996) model,

as a proxy for the amount of information-based stock trading. We decompose this PIN measure

2Our 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 which is open

and accessible (with a cost). Due to 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 Section 2, certain technical features make it

less feasible to calibrate Holmstrom and Tirole’s model and to empirically test their model prediction.

2

into two orthogonal components: one is risk-related and the other 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 have been a paucity of

attempts on model calibrations. Lambert, Larcker, and Verrecchia (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). In a framework that

3

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 Section 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, Goldstein, and Jiang (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 the 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.

3Theoretical 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).

4

2 The Model

Holmstrom and Tirole (1993) (HT, hereafter) are among the first to combine the stock price

formation process with the optimal contracting process. HT 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 HT highlights the importance of market

microstructure in inducing executive incentives, it is not easy to calibrate the HT 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.5

2.1 Economy

We begin with a single-period model with two points of time, indexed =0, 1. The period is further

divided into several stages. We summarize the time line of the model in Figure 1:

=0:Public firm established

- 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

=1:Terminal payoff realized;

incentive contract honored;

firm liquidated?

6 6?

Figure 1: The Time Line

At the initial point of time 0, a publicly held firm is established and shares are issued on the

4 In the HT 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, while the traditional principal-agent model treats

the volatility as a measure of uncertainty, the HT model assumes that stock price volatility conveys the precision of

informed traders’ information, which is difficult to quantify.5Based 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).

5

firm’s future cash flow. The terminal payoff of the firm at time 1 is e = +, where 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 .

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 and the firm’s terminal

payoff e: = + + e (1)

where represents the fixed salary, and capture the sensitivities of the manager’s compensation

to and e, respectively. The compensation contract in equation (1) follows a commonly adoptedform in the literature (see, e.g., Holmstrom and Milgrom, 1987; Holmstrom and Tirole, 1993; and

Baiman and Verrecchia, 1995). Given the compensation contract, the manager chooses an effort

level ∈ [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 non-contractible 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

is + , where is i.i.d. with mean zero and variance . Informed trader submits a market

order that is linear in her signal, ( + ). 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 and is a normally distributed variable with mean zero and variance . We also

assume that there are informed investor and is an endogenous number. The total order flow

observed by the market maker is = +P

=1() + . The competitive market maker, given

the aggregate order flow , sets a price such that = [e|].86Murphy (1999) provides a criticism on the standard principal-agent 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.7This assumption is innocuous as, in real world, managers are subject to many rules and restrictions to trade

stocks, particularly stocks of the companies under their management.8We use the firm’s gross proceeds instead of the net proceeds in the pricing function so as to obtain analytically

tractable solutions. Because in our model is linear in both and , factoring 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, = [( − )|] (see alsoBaiman and Verrecchia 1995; and Milbourn 2003).

6

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 with the (absolute) risk aversion

coefficient . Her cost of choosing the effort is denoted as () = 122. The cost is measured

in money and is independent of the manager’s wealth. Given her choice of effort , the manager’s

evaluation of the normally distributed income can be represented in the certainty equivalent

measure as follows:

( ) = ( )−

2 ( )− () (2)

2.2 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 = + (Kyle 1985). Using standard techniques, we obtain the equilibrium value of

as = − 12

Γ12 , where Γ =

2(+)

[(+1)+2]2 . The expected profit of an informed trader is given by

=(+)

12

12

12 [(+1)+2]

. 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

is determined by

( + )12

12

12 [( + 1) + 2]

= (3)

We then analyze the incentive contract. Following Holmstrom and Tirole (1993), we transform

the wage function into the following equivalent normalized form:

= + + (4)

where = + ∗, = e − ∗, and ∗ 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 analytically easier with the normalized wage equation, so we build our

7

analysis on this transformed compensation function from this point onwards. One way to interpret

equation (4) is that besides the stock price , the principal observes another signal, , and include

the signal into the compensation contract. The zero-mean 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:

Lemma 1 In the rational-expectations equilibrium, the compensation contract can be re-written as

= + ( − ( )

()) (5)

with = −() ()

. The equilibrium pay-performance sensitivity is given by

=1

1 + ( )(1− 2) (6)

where ≡ ( ). The equilibrium effort level ∗ is given by

∗ =

(7)

In equilibrium, is negative because is positive (see Lemma 3). The intuition is similar to

the relative performance argument in Holmstrom and Milgrom (1987). By construction, acts as

one signal, in addition to the stock price , to help the principal better extract the information

about the managerial effort. If is high then the principal knows that the exogenous shock is

positive, and hence 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 ≡ − ( )

(). We can view as an aggregate performance index built on two

performance measures, and . The compensation scheme in our model is hence based on an

aggregate measure that captures various aspects of a firm’s performance.10

9 In order to interpret as a reliable signal on reported accounting earnings, we have to assume that the managertruthfully reports earnings. Factoring the manager’s incentives to misreport earnings only makes noisier but does

not change our results qualitatively because, by construction, only plays the role of a signal.10Executive compensation contracts in real world are oftentimes written on a variety of performance measures such

8

2.3 Properties of Equilibrium

Lemma 2 The number of informed traders, , increases as the uncertainty of the firm’s cash flow,

, 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 from collecting the costly private signal and becoming an informed trader increases as

the uncertainty of the firm’s cash flow increases, which can been easily shown since |= 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 , increases.

Lemma 3 The correlation coefficient is positive. Moreover, both 2 and ( ) are increasing

functions of the underlying uncertainty .

Lemmas 1—3 imply that as the underlying uncertainty 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 ( ) ≡ ( )(1 − 2). The overall response of the optimal pay-

performance sensitivity to the change in the fundamental uncertainty is given by

=

−[1 + ( )]2

( )

(8)

where

( )

= − (9)

with

= ( )

=

( + 1) 3 + 6 2 + 82

[( + 1) + 2]3 0 (10)

and

= ( )

=

2 ( + 2)[( − 1) − 2][( + 1) + 2]3

(11)

as economics value added (EVA), return on invested capital (ROIC), total returns to shareholders (TRS), and etc.

The aggregate measure we propose in equation (5) thus reflects the features of the incentive pay scheme in real world.

9

0 if +2

. Moreover, the term strictly dominates the term, and ( )

0.

Proposition 1 shows that two offsetting effects arise out of a growing uncertainty. The

term measures the direct effect of an increase in uncertainty on incentives for a fixed number of

informed traders. In sharp contrast, the 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 term thus characterizes the effect of

the information-based trading on incentives.

Combining Proposition 1 with Lemma 1, we obtain

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 effect) than for firms with

a low level of information-based stock trading (or a low effect).

Proposition 2 implies a negative risk-incentive relation even after taking into account the

effect. equals zero if is a constant (i.e., no risk-driven information-based trading). When

is zero, the term alone, measuring the traditional risk-incentive tradeoff, captures the overall

risk-incentive relation. In the presence of information-based stock trading, the 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

information-based stock trading via a welfare analysis.

3.1 Calibration: Baseline Values

Exogenous parameters in this model consist of the absolute risk aversion coefficient , the parameter

on manager’s disutility of effort , the cash flow variance , the signal noise variance , the

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liquidity order variance , and the reservation utility of becoming an informed trader . We

normalize , and by the scale of and define ≡ , ≡

and ≡

, respectively.

We calibrate the parameters of our model based on a data set merging the CRSP, Compustat,

ExecuComp, and Thomson Financial’s Institutional Holding databases over 1992—2005. 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, and are the mean and variance of a firm’s payoff,

respectively. Measuring the payoff by the firm’s market value, we set to the sample mean of

the firm market value, i.e., = 610547. Since 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 ($594,632.75

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 0 = 2628062. 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 zero to 27,266.16 million shares.

Therefore, we calculate the volatility in trading volume as the time-series 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 101.85 (million shares), so we set the variance of the total order

flow = 101852 = 1037367. Moreover, it is well accepted in the literature that institutional

investors are informed traders, so we set the number of informed traders to the average number

of institutional investors for our sample firms, which is 164.11 Finally, we follow the literature to

choose values of the risk aversion coefficient ; we set 0 = 2 (e.g., Haubrich 1994).12

Using a multi-step internally consistent approach (see Appendix 2), we achieve convergence in

calibration when we set 0 = 0042, 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

11There 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 under-estimate 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.12There is a typo in Haubrich (1994), pp.274, where is said to equal four. However, based on the assumed values

for the other parameters and the implied pay-performance sensitivity of 0.00621, it can only be the case that = 2.

11

Murphy, 1990). This value is close to our sample mean (Panel A of Table 1; see also Table I

of Aggarwal and Samwick 2003) as well as the OLS estimates of PPS in the literature (see, e.g.,

Aggarwal and Samwick 1999; Murphy 1999). The parameter on the manager’s disutility of effort,

0, is calibrated to be 68791 − 6. As a result, the manager’s disutility of choosing the effort is() = 1

22 = 12821 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 (A.1) in Appendix 1). 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 top-executive compensation amounted to about 5% of the companies’ net income for

the 1993-1995 period and the ratio rose to 9.8% in the 2001-2003 period. The ratio 0, which

measures the relative importance of the noise term in the informed trader’s signal, equals 54.21.

This ratio suggests that about 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 0 = 30330−4, and in turn, we calculate the variance of liquidityorders = 209477, 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, 0, is 36957−5, implying that the reservation value to become an informedtrader is 225.25 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 225.25 units, which is translated

into about 4.18% of the average market value of firms.

3.2 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

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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 allowing the underlying uncertainty

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 from equation (3). Consistent with Lemma 2,

increases monotonically, from the initial level of 164 to 197 when doubles and further to 209

when triples. As Proposition 1 predicts, both and are positive and is smaller than

( is positive because 1 + 20 = 109 in this exercise). The ratio of over rises

monotonically from the initial level of 9.18% to 22.78% when doubles, and this ratio climbs

further to 27.95% when triples. Moreover, the gap between the two effects narrows as the

underling uncertainty mounts, indicating an increasingly stronger offset of the effect relative to

the effect.

At equilibrium, the manager’s ex-ante utility is fixed at = , and the principal’s ex-ante

utility is = ( − ) = − 2

2 ( )− 2

2 ()− ( )− 2

2− . (See proof of

Lemma 1 in Appendix 1). The social welfare is the sum of the principal’s ex-ante utility and the

manager’s ex-ante utility:13

=

− 2

2 ( )− 2

2 ()− ( )− 2

2

=

− 2

2 ( )(1− 2)− 2

2 (12)

For the welfare analysis, we examine the following two scenarios:

1. = 0, where 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 0 existing informed traders.

13Since 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 term defined in

equation (12) is the social welfare for the entire economy including both the real and financial sectors.

13

2. 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 1 and 2 represent the levels of social welfare in Scenarios 1 and 2, respectively. We

calculate 1 and 2 using the baseline values of the 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 1 and 2, respectively. Both 1 and 2 are

strictly downward-sloped, indicative of a tradeoff 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 tradeoff as well as a negative risk-welfare

relation. Strictly dominated as it is, the information enhancement effect contributes to a significant

welfare improvement. In the figure, the 2 curve tops the 1 curve, and the gap widens as

the uncertainty mounts. Starting from the same initial level, 2 exceeds 1 by 9.80% when

doubles, and by 17.14% when triples.

To measure the social welfare improvement due to the information enhancement, we compute

the difference between the decline in 2 and the decline in 1 as a result of the increases in

, and then divide the difference by the magnitude of the decline in 1 to obtain the percentage

offset of the risk-welfare tradeoff. Figure 2, Panel B plots the percentage offsets of the social

welfare reduction against percentage increases in uncertainty . The offset gains in strength as

the underlying uncertainty builds up. When rises by 1% from the initial value, the offset is

9.38%. The offsets reach 17.96% and 20.29% when doubles and triples, respectively.

4 Empirical Analysis

To offer more direct evidence, we empirically study in this section the impact of information-based

stock trading on CEO incentives and the risk-incentive relation.

4.1 Data and Variables

Data for this empirical study are from several sources. CEO compensation data come from the

ExecuComp database; 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

14

the data of probability of informed trading (), which is constructed from intraday trading data

of the TAQ database; we extract institutional ownership information from the Thomson Financial

Institutional Holdings Database. Due to 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 , 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 Section 4.2

the detailed discussions of this regression (i.e., equation (14)). We calculate the change in CEO’s

firm-specific wealth ( ), 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 ( ); 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 ( ) for a given year, we first obtain the firm value

( ), in million dollars, as the product of fiscal year-end stock price and the total number

of shares outstanding, and we then calculate as that year’s inflation-adjusted annual stock

return ( ) multiplied by the beginning-of-year firm value. Thus, 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 over $594 billion. As a result, the change in shareholder

value, , 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 are

15

respectively a loss of over $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 is 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 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 30.188, a median of 7.539, and a standard deviation of

64.649.

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, . We compute in a given year as

the annualized standard deviation in the past five-year inflation-adjusted monthly stock returns

() multiplied by the beginning-of-year 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 , as the proxy for the amount of information-based stock

trading.14 Table 2 presents summary statistics of the two key variables. Notably, is severely

skewed to the right.

14We 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, Hvidkjaer, and O’Hara (2002).

16

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 define as the total institutional share holdings in proportion of the total number

of shares outstanding, and 5 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 () 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 investment-to-capital ratio ( ) as capital

expenditure (data 128) divided by fixed assets (data 8), and the leverage ratio ( ) 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). Further, to characterize the impact of a firm’s

financial constraints on CEO incentives, we follow Kaplan and Zingales (1997) to construct the KZ

index (). Other control variables include CEO tenure (), and dummies for each year

and each industry (). To capture the potential nonlinear relation between CEO incentives

and CEO tenure, we use the logged value of the CEO’s tenure () in our empirical analysis.

Table 2 summarizes these control variables except .

4.2 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.

4.2.1 Decomposition of PIN

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 information-based stock trading, , may contain components which help

17

improve CEO incentives but are unrelated to risk. To address this concern, we separate into

two components, one related to risk and the other not, by running the following cross-sectional

regression on a yearly basis:15

= 0 + 1 ∗ + 2 ∗ + (13)

where is the logarithm value of a firm’s market capitalization. We use the fitted values

( ) and the residuals () of the year-by-year cross-sectional regressions to measure the

two components of that are related and unrelated to risk, respectively.

This PIN decomposition model deserves a further discussion. Besides the dollar return

risk measure , we include firm size in the decomposition regressions for two reasons.

First, because our risk measure is mechanically and positively correlated with firm size,

which is well-known to significantly and negatively correlate with (Easley, Hvidkjaer, and

O’Hara, 2002), a univariate regression of on yields a significantly negative coefficient

estimate on . The negative loading of on in the univariate regression appears

to be dominated by and pick up only the impact of firm size on even though is positively

and significantly correlated with the percentage return risk measure .16 Therefore, we

believe that in the bivariate regression like equation (13), the coefficient estimate on correctly

captures the impact of risk on information-based 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 from equation (13) includes the firm size element which is well-known to be negatively

related to pay-performance sensitivities (e.g., Schaefer, 1998). As a result, our estimation using

this 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 1992-2004 period. It

is clear that, consistent with the literature, is inversely related to firm size (Easley, Hvidkjaer,

15 In an earlier draft, we include the squared instead of in the regressions to capture the potentially

non-linear relation between and . 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.16 In fact, if we run a bivariate regression of on and , the coefficients estimates on

and are significantly negative and significantly positive, respectively.

18

and O’Hara, 2002) – the coefficient on is negative each year. The table also shows that

is positively correlated with firm risk after controlling for firm size: the coefficient on

is positive for almost all years except 1992. The adjusted 2 of the decomposition regression

average at 0.386 over the sample period and show an increasing trend, jumping from below 0.40 in

the 1990s to over 0.60 after 2000.

4.2.2 Econometric Models

Using the two components, we follow Jensen and Murphy (1990) and Aggarwal and

Samwick (1999) to specify our main econometric model as follows:

= 0 + ∗ (0 + 1 + 2−1 + 3−1 +X≥4

)

+1 ∗ + 2 ∗ −1 + 3 ∗ −1 +X≥4

∗ + (14)

In this specification, and represent respectively the information-based stock trading

related and unrelated to firm risk; includes the set of control variables such as

−1, 5−1, −1, −1, −1, −1, , year dummies, and

industry dummies.

Equation (14) implies that we can calculate the pay-performance sensitivity (PPS) as:

= 0 + 1 ∗ + 2 ∗ −1 + 3 ∗ −1 +X≥4

∗ (15)

In equation (15), 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 tradeoff driven by the risk-related component

of information-based stock trading. Thus, the overall risk-incentive relation based on equation (14)

19

is equal to 1 + 2

. Accordingly, the size of the offset is measured as the absolute value of

2

1.

Table 2 shows clear evidence on the presence of extreme outliers in the data, particularly on CEO

compensation , firm risk , and pay-performance sensitivity . 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.

For robustness check, 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 heteroscedasticity-robust 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

against variables of interest and control variables (e.g., Core and Guay, 1999; Jin, 2002).

Consequently, we estimate equation (15) with both median regressions and CEO-firm fixed-effect

OLS regressions.

4.3 Empirical Results

Table 4 presents the estimation results for the two models, with Columns 1-2 corresponding to

equation (14) and Columns 3-4 to equation (15). We start with the median regression results for

equation (14). The coefficient estimate on the firm risk is negative and significant at the 1%

level, consistent with the standard agency theory. The coefficient estimate on 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 is positive and significant at

the 1% level, suggesting that the non-risk-related component of information-based 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 and because the overall

20

risk-incentive relation is equal to 1+2

. Table 3 reports that the average loading of

on is 9.39e-7, that is,

= 939− 7. Given a negative coefficient estimate on

and a positive coefficient estimate on 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 by2

1and is economically meaningful.

Using the median regression estimates, a one-standard-deviation increase in causes a

direct reduction of CEO incentives by 887 − 5 × 666224 = 0591; meanwhile, this increase in

causes an indirect improvement in CEO incentives through information-based trading by

00063 × 7585 = 0475 because the increase in causes to increase by 939 − 7 ×666224 = 00063. The percentage of the offset is 0475

0591= 8030%.

The two positive coefficient estimates affiliated with the two 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 non-trivial 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 and are respectively negative and positive and both are significant at the 1%

level; the estimated coefficient on is positive but nonsignificant. Using the OLS estimates,

we compute the percentage of the offset of the risk-incentive tradeoff as 939−7∗10418226−4 = 4329%

as a one-standard-deviation increase in causes a direct reduction of CEO incentives by

2.26e-4*6662.24=1.506 and an indirect improvement in CEO incentives by 0.0063*104.18=0.656.

We proceed to examine the estimation results for equation (15). The results are similar. For

21

example, is significantly and negatively related to firm risk , supporting the risk-

return tradeoff predicted by the standard agency theory. 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 causes a direct reduction of CEO incentives

by 382−4×666224 = 2545; this increase in also causes an indirect improvement in CEO

incentives via the information-based trading by 00063× 214893 = 1354, resulting in an offset of13542545

= 5282%. Using the OLS estimates, a one-standard-deviation increase in causes a

direct reduction of CEO incentives by 376− 4× 666224 = 2505 and an indirect improvement inCEO incentives by 00063× 323893 = 2041, resulting in an offset of 2041

2505= 8089%.

5 Summary and Conclusions

In this paper we investigate the role of information-based stock trading in affecting the risk-incentive

relation. We construct a parsimonious principal-agent 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 tradeoff given a level of information-based trading; and the indirect effect reflects incentive

enhancement due to the risk-related information-based stock trading. This information-production

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 tradeoff. The numerical analysis illustrates that the risk-related information-based

22

trading offsets about 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 tradeoff by 43%

to 81%.

Our study not only highlights the important and under-studied role of the risk-related

information-based 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 co-exist.

23

Appendix 1: Proofs

Proof of Lemma 1: We set up the principal’s problem as follows:

max

(e − )

s.t. max

( )−

2 ( )− () ≥ (A. 1)

where is the reservation utility to the manager. Given the compensation contract =

+ + (as specified in equation (4)), the manager solves the following problem:

max

+ − 2

2 ( )− 2

2 ()− ( )− 2

2 (A. 2)

The first-order condition yields

= (A. 3)

We therefore have equation (7). At equilibrium, the manager’s individual rationality condition

should be binding, which yields

= − +2

2 ( ) +

2

2 () + ( ) +

2

2 (A. 4)

With = + + , the principal’s problem can be rewritten as

max

(1− )−

s.t. =

= − +2

2 ( ) +

2

2 () + ( ) +

2

2

Substitute for and equation (A. 4) for . The above problem is therefore simplified as

max

− 2

2 ( )− 2

2 ()− ( )− 2

2 (A. 5)

The first-order conditions yield

1

− ( )− ( )−

= 0 (A. 6)

and

− ()− ( ) = 0 (A. 7)

We immediately obtain from equation (A. 7)

= −( ) ()

(A. 8)

24

Plugging = −() ()

back into equation (A. 6), we obtain

=1

1 + (1− 2) (A. 9)

Q.E.D.

Proof of Lemma 2: Using the implicit function theorem, we have:

= 12 2(+)

− 12

12 +4

12

[(3+1)+2]=

(+1) 2+6+4

2

(+)[(3+1)+2] 0 Q.E.D.

Proof of Lemma 3: Because = +P

=1()+ , we obtain =(+1)+2

+. Further,

with = + , we have ( ) = 2 = 2

(+1)+2.

From the stock market equilibrium, we have ( ) = ( ) = =

2

(+1)+2= ( ). Then, 2 ≡ 2()

( )=

(+1)+2. Thus, 2

=

(+2)

+2

[(+1)+2]2 0

because

0 (see Lemma 2).

We then conclude that ( ) = 2, and clearly, ( )

0 as 2

0 Q.E.D.

Proof of Proposition 1: Using the results from proof of Lemma 3 and applying the total

differentials, we immediately obtain ( )

≡ ( )(1−2)

= − , where and

are defined as in equation (10) and equation (11), respectively. To show that ( )

0, we

need to show that . That is,

( + 1) 3 + 6 2 + 82 2 ( + 2) [( − 1) − 2]

(A. 10)

Or,

≡ £ ( + 1) 3 + 6 2 + 8

2

¤[( + ) (3 + 1) + 2]

≡ ( + 2) [( − 1) − 2]£( + 1) 2 + 6 + 4

2

¤ (A. 11)

This holds as the coefficient of each term in is larger than that of its corresponding term in

. Q.E.D.

Appendix 2: The Calibration Method

Given the chosen values for the parameters/variables as reported in the upper half of Panel B

of Table 1, we adopt the following internal-consistent multi-step approach to calibrate the values

of the other parameters as they do not have good empirical estimates.

Step 1. We choose one initial value of the pay-performance sensitivity, . From equation (7) we

25

calculate = given .

Step 2. Defining ( ) ≡ ( )(1 − 2), and using the proof of Lemma 3 (available in

Appendix 1 of the online supplement), we derive that

( ) = 2 ( + 2)

[( + 1) + 2]2=

(1 + 2)

[( + 1) + 2]2 (A. 12)

Combining equation (6) with equation (A. 12), we obtain

1− 1

= (1 + 2)

( + 1 + 2)2 (A. 13)

Given , , , and , we solve for from equation (A. 13).

Step 3. Using = +P

=1() + , we derive

=( + 1) + 2

+ (A. 14)

which yields

≡

=

+

( + 1) + 2

=

1 +

( + 1) + 2

(A. 15)

We then obtain .

Step 4. We rewrite equation (3) as

=(1 + )

12 ()

12

12 ( + 1 + 2)

(A. 16)

from which we calculate .

Step 5. Given these calibrated parameter values, we recalculate ( ) from equation (A.

12), and then we calculate from equation (6). We use step 5 to check for the convergence of the

calibration. If the value of calculated from step 5 is significantly different from the chosen initial

value in step 1, then we pick another initial value and repeat step 1 to step 5 until the two

values are close to each other (with a difference less than 1e-10).

26

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29

Table 1: Summary Statistics of Data and Baseline Values of Calibrated Parameters/Variables

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 year-end 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/variables.

Panel A: Relevant Summary Statistics of Data

Variables Mean Std Dev Median Min Max

Firm Value ($M) 6,105.47 21,129.80 1,243.46 8.49e-3 594,632.75

Uncertainty in Firm Value ($M) 2,628.06 9,112.40 518.58 3.52 242,779.90

Trading Volume (M shares) 281.18 1,096.75 67.34 0 27,266.16

Volatility in Volume (M shares) 101.85 317.18 29.68 1.37e-3 8,857.92

Number of Institutional Investors 163.74 159.01 117 1 1,409

incentives (PPS) 37.152 72.465 10.719 0 1000

Panel B: Baseline Values

Parameters/Variables Calibrated Values

≡ () 6,105.47

0 ≡ () 2,628.062

101.852

0 164

0 2

0 0.042

0 6.8791e-6

0 ≡

54.21

0 ≡

3.6957e-5

0 ≡

3.0330e-4

30

Table 2: Summary Statistics of Data for Regression Analysis

We obtain the firm value ( , in millions of dollars) as the product of fiscal year-end stock price and

the total number of shares outstanding. We denote by the logarithm value of firm value. We calculate

the change of firm value ( ) in a given year as that year’s inflation-adjusted annual stock returns

( ) 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 ( ), and we compute of a given year as

the annualized standard deviation of the past five-year inflation-adjusted monthly stock returns ( )

multiplied by the beginning-of-year firm value (in millions of dollars). We use Duarte and Young’s (2009)

adjusted probability of informed trading () measure, which is developed from an extended version of

Easley, et al.’s (1996) structural microstructural model, to measure the amount of information-based stock

trading. The two variables, and , are separately the fitted values and residuals from year-by-

year cross-sectional regressions of against and (see Table 3 for details). We calculate

aggregate institutional holding () as the total institutional share holdings scaled by the total

number of shares outstanding. We compute the concentrated ownership (5) as the top-five institutional

share holdings in proportion of the total institutional share holdings. We calculate Tobin’s Q ()

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 ( ) as capital expenditure (data 128) divided by fixed assets (data 8),

and the leverage ratio ( ) 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 () as a measure of financial constraint. We calculate the CEO

total compensation ( ), 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 as

a CEO’s tenure as of year , and as the logarithm value of the CEO’s tenure. The stock-based

pay-performance sensitivity () 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 , which has 10,166

observations.

31

Variables Mean Std Dev Median Min 1% 25% 75% 99% Max

MKTVAL ($M) 8,183.08 24,159.12 1,969.07 1.670 58.434 704.99 5786.29 117,393.3 594,632.8

SIZE ($M) 7.652 1.585 7.585 0.513 4.068 6.558 8.663 11.673 13.296

ANNRET 0.171 0.835 0.109 -0.962 -0.703 -0.099 0.335 1.905 50.033

ANNVOL 0.362 0.164 0.328 0.100 0.132 0.250 0.434 0.937 1.617

VCHGE ($M) 659.76 7,061.23 119.99 -162,751.9 -13,204.56 -117.15 690.96 22,743.53 209,795.1

STDV ($M) 2,296.11 6,662.24 603.86 3.522 33.111 236.85 1,658.60 32,185.88 145,964.1

PIN 0.133 0.047 0.125 0 0.054 0.099 0.158 0.278 0.468

PINF 0.133 0.033 0.134 0.030 0.056 0.112 0.155 0.204 0.245

PINR -1.67e-3 0.049 -4.15e-3 -1.197 -0.084 -0.019 0.013 0.114 0.340

TOTHLD 0.584 0.198 0.608 4.73e-5 0.029 0.456 0.730 0.956 0.9998

CON5 0.427 0.145 0.402 0.128 0.197 0.327 0.495 0.956 1

TOBIN 1.787 1.272 1.411 0.435 0.777 1.114 1.976 6.994 45.332

INV 0.211 0.189 0.178 0 0.018 0.114 0.266 0.688 9.334

LEV 0.423 2.457 0.405 -73.171 0 0.234 0.545 1.175 253.31

KZ 5.897 9.809 3.362 -0.024 0.361 2.237 5.364 63.612 81.951

COMP ($K) 20,319.32 235,034.5 4,038.42 -7.24e+6 -100,259.3 1,141.15 12,545.33 337,894.7 1.42e+7

TENURE 7.636 7.560 5 1 1 3 10 39 55

LNTEN 1.605 0.938 1.609 0 0 1.099 2.303 3.638 4.007

PPS 30.188 64.649 7.539 0 0.095 2.170 24.685 354.01 646

Table 3: PIN Decompositions

This table reports the results of annual cross-sectional regressions to decompose the proxy for the amount

of information-based stock trading, , against firm size, , and firm risk, . The variables are

defined as in Table 2. The regressions are estimated year-by-year over the period from 1992 through 2004,

and we denote by and the fitted values and the residuals of the regressions, respectively. The

last row reports the average values of each estimate across the 1992-2004 period.

PINF PINR

Year Intercept SIZE STDV Adj. R2 Nobs Mean Median Std Dev Mean Median Std Dev

1992 0.297 -0.018 -4.44e-7 0.325 932 0.166 0.167 0.026 -1.18e-3 -1.53e-3 0.054

1993 0.303 -0.020 1.42e-6 0.267 1120 0.161 0.162 0.025 -1.03e-3 -3.67e-3 0.055

1994 0.295 -0.020 1.76e-6 0.240 1160 0.155 0.155 0.025 -9.41e-4 -4.15e-3 0.056

1995 0.272 -0.016 2.08e-6 0.191 1201 0.154 0.154 0.021 -9.57e-4 -4.44e-3 0.055

1996 0.274 -0.016 1.32e-6 0.236 1232 0.152 0.153 0.022 -9.60e-4 -3.98e-3 0.052

1997 0.233 -0.013 1.27e-6 0.208 1244 0.134 0.134 0.017 -9.11e-4 -5.50e-3 0.047

1998 0.233 -0.014 6.66e-7 0.276 1291 0.125 0.126 0.021 -9.01e-4 -5.75e-3 0.047

1999 0.248 -0.016 4.82e-7 0.376 1219 0.124 0.126 0.025 -9.29e-4 -4.13e-3 0.046

2000 0.240 -0.016 2.30e-7 0.409 1138 0.120 0.121 0.027 -9.85e-4 -4.49e-3 0.047

2001 0.289 -0.022 4.56e-7 0.607 1099 0.122 0.122 0.034 -1.04e-3 -1.75e-3 0.044

2002 0.278 -0.022 4.86e-7 0.625 1124 0.114 0.114 0.034 -1.03e-3 -2.08e-3 0.043

2003 0.283 -0.023 1.56e-6 0.646 1108 0.109 0.109 0.030 -1.06e-3 -2.23e-3 0.041

2004 0.263 -0.021 9.16e-7 0.617 1065 0.099 0.100 0.028 -1.04e-3 -2.48e-3 0.041

Average 0.270 -0.018 9.39e-7 0.386 1149 0.133 0.134 0.026 -0.001 -0.004 0.048

32

Table 4: Regression Results

This table reports the estimation results of the following two models:

= 0 + × (0 + 1 ∗ + 2 ∗ −1 + 3 ∗ −1 +≥4

∗ )

+1 ∗ + 2 ∗ −1 + 3 ∗ −1 +≥4

∗ +

= 0 + 1 ∗ + 2 ∗ −1 + 3 ∗ −1 +≥4

∗ +

Here, and , are separately the fitted values and residuals from year-by-year cross-sectional

regressions of the proxy for the amount of information-based stock trading, , against and

(see Table 3 for details). The control variables include −1, 5−1, −1,−1, −1, −1, , 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 1993-2005. *, **, *** stand for statistical significance at the 10%, 5% and 1% levels,

respectively.

33

Model 1 (Dep. Var. is COMP) Model 2 (Dep. Var. is PPS)

Parameters Median Regression OLS-FE Regression Median Regression OLS-FE Regression

Intercept 4611.89*** 21070.31* -38.341*** -28.032**

(480.99) (11703.24) (1.293) (10.869)

VCHGE -9.689*** -6.518***

(0.114) (2.414)

VCHGE*STDV -8.87e-5*** -2.26e-4***

(1.08e-6) (2.63e-5)

VCHGE*PINF 75.850*** 104.18***

(0.759) (20.406)

VCHGE*PINR 7.160*** 0.797

(0.195) (3.899)

VCHGE*TOTHLD 1.083*** 1.151

(0.057) (1.485)

VCHGE*CON5 2.402*** 1.789

(0.079) (1.629)

VCHGE*TOBIN 0.067*** 0.166*

(0.003) (0.086)

VCHGE*KZ -0.019*** 5.98e-4

(0.001) (0.026)

VCHGE*LEV -1.433*** -2.790***

(0.033) (0.804)

VCHGE*INV 3.345*** -0.660

(0.068) (2.204)

VCHGE*LNTEN 1.285*** 1.422***

(0.007) (0.241)

VCHGE*Dummies Yes Yes

STDV 0.915*** 1.591** -3.82e-4*** -3.76e-4**

(0.013) (0.612) (3.11e-5) (1.90e-4)

PINF -31497.89*** -78872.23 214.893*** 323.893***

(2331.59) (64867.38) (6.286) (57.241)

PINR 935.266 2479.57 13.089*** 21.385***

(804.30) (12185.03) (2.135) (7.413)

TOTHLD 792.98*** -10949.44** -7.454*** -10.340***

(249.94) (4942.81) (0.689) (3.530)

CON5 387.32 -2932.58 4.493*** -4.789

(351.25) (4786.32) (0.976) (4.279)

TOBIN 351.60*** 529.89 1.587*** 1.909***

(34.64) (821.38) (0.094) (0.632)

KZ 10.927** 3.941 -0.059*** -0.066

(4.853) (90.64) (0.013) (0.069)

LEV 513.03*** 668.17* 5.12e-4 0.102

(12.88) (359.39) (0.013) (0.083)

INV 1469.5*** -1328.20 11.719*** 5.413*

(196.23) (2597.04) (0.769) (3.310)

LNTEN 597.57*** 2366.04 6.134*** 6.268***

(42.47) (1452.36) (0.121) (1.354)

Dummies Yes Yes Yes Yes

Sample Size 11,795 11,795 10,166 10,166

2/Pseudo 2 0.193 0.293 0.112 0.146

34

Figure 2: Responses of Social Welfare to Changes in Uncertainty : Baseline Values

Panel A plots different levels of social welfare in response to percentage changes in the underlying uncertainty

. The dashed line (1) and the solid line (2) represent the social welfare responses for the cases

= 0, and changes according to equation (3), respectively. Panel B plots the percentage offsets of the

social welfare reduction against percentage increases in uncertainty . We compute the difference between

the decline in 2 and the decline in 1 as a result of the increases in , and then divide the difference

by the magnitude of the decline in 1 to obtain the percentage offset of the risk-welfare tradeoff.

Panel A. Responses of to percentage increases in

0 20 40 60 80 100 120 140 160 180 2001600

1800

2000

2200

2400

2600

2800

3000

3200

Soci

al w

elfa

re

% increase in uncertainty

Panel B. Percentage offsets of the risk-welfare tradeoff

due to information enhancement

0 20 40 60 80 100 120 140 160 180 2008

10

12

14

16

18

20

22

% o

ffse

t in

soci

al w

elfa

re r

educ

tion

% increase in uncertainty35