Risk-Sensitive CEO Contracts Gonzalo Morales˚ Job Market Paper

January 2015

:

[latest version]

Abstract This paper studies the compensation structure and firing policy of contracts for risk-averse managers implied by a dynamic moral hazard model with sizeable risk premia. Due to the unobservability of effort and the dynamic contracting framework, managers are incentivized by a mix of short- and long-term compensation, and the threat of being fired. Since firms are heterogeneously exposed to aggregate risk, the timing of compensation and termination policy differs between firms. When shareholders are averse to uncertainty about long-term growth prospects and the managers receive disutility from effort, the model can explain the negative relation between aggregate risk and long-term compensation. Also, the model generates procyclical aggregate turnover. In short, this paper highlights the importance of risk premia in understanding the dynamics of CEO contracts.

˚

University of British Columbia. E-mail: [email protected]. website: sites.google.com/site/gonzalomorales : I am extremely grateful for advice and encouragement from my advisors Ron Giammarino and Howard Kung. I also thank Kai Li for comments that improved this paper. I have also benefited from comments by Jan Bena, Murray Carlson, Joao Cocco, Lorenzo Garlappi, Francisco Gomes, Hernan Ortiz-Molina, Jose Pizarro, Ercos Valdivieso, and seminar participants at UBC for helpful comments. All errors are my own.

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Introduction

In the last decades a vigorous debate has risen among shareholders, stakeholders, regulators, and news media. They have questioned whether the high level of compensation can be justified as the reward needed to incentivize the managers, or instead the compensation corresponds to rent extraction by the managers. The empirical literature has found (Garvey and Milbourn (2006); Bertrand and Mullainathan (2001)) that their remunerations increase with positive events that are out of their control (e.g. positive aggregate shocks). Furthermore, Garvey and Milbourn (2003), and Jin (2002) find a negative effect of aggregate risk on stock-based compensation for young managers and for managers with short-selling constraints, respectively. Also, Bushman, Dai, and Wang (2010) find that forced turnover is negatively related with firms’ exposure to aggregate risk. This evidence is difficult to rationalize in a static principal-agent model, which shows that exogenous shocks should be filtered out while analyzing the remuneration of executives (H¨olmstrom (1979)). The current paper proposes a dynamic agency model to rationalize remuneration and turnover, and their relation with risk premia. To study the effects of risk premia on executive compensation and turnover I develop a dynamic moral hazard model with several key features. First, the economy is subject to aggregate shocks, which are observable for all agents in the economy. Second, firms are heterogeneous in their exposure to aggregate risk. Third, the representative shareholder is risk-averse and sensitive to uncertainty about long-term growth prospects. Fourth, CEOs are risk-averse and their effort is unobservable. Fifth, an incumbent CEO can be replaced, if it is optimal. The model is calibrated to match salient moments of contracts and returns: (i) the ratio of expected cash compensation to expected change in equity compensation, (ii) the ratio of the standard deviation of cash compensation to the standard deviation of the change in equity compensation, (iii) the correlation between cash compensation and (iv) the change in

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equity-based compensation and the value premium.1 The calibrated model explains in the cross-section the negative relation of risk premia with equity-based compensation and forced turnover. Also, the model explains the procyclicality of aggregate turnover. In the present framework, each firm needs the effort exerted by its CEO to produce, which is unobservable. The representative shareholder (“she”) and the CEO (“he”) enter into a long-term contract to incentivize him. The contract specifies: short-term compensation, long-term compensation, and a replacing policy of the manager. The manager is incentivized by linking his compensation to realized cash flows. Thus, the manager’s compensation increases with high profits and decreases with low profits. This means that with high profits the incentives problem is relaxed but with low profits the incentives problem is more severe. In contrast to a static setting where exogenous observable shocks should not affect the manager’s remuneration (H¨olmstrom (1979)), aggregate shocks will affect manager’s compensation as long as they persistently affect the profitability of the firm (DeMarzo, Fishman, He, and Wang (2012); Piskorski and Tchistyi (2010); Hoffmann and Pfeil (2010)).2 This generates that during expansions, when profits are high, the incentives problem is relaxed. However, during recessions the incentives problem is more severe. For the representative shareholder it is costly that the incentives problem is more severe during recessions, because her marginal utility increases with negative aggregate shocks. Thus, agency costs are high precisely when the marginal utility of the representative shareholder is high. Since firms are heterogeneously exposed to aggregate risk, they have different compensation structures and replacement policies. Firms with high exposure to aggregate shocks have higher revenue volatility and need to increase the exposure to aggregate risk of their managers (relatively to managers at low exposure firms) to incentivize them, increasing the volatility of their compensation. However, firms with high exposure to aggregate risk will reduce their managers’ long1

Along the paper I refer to short-term compensation as cash compensation and long-term compensation as equity portfolio compensation, indistinctively. 2 Because a manager’s compensation is related to the profitability of the firm.

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term compensation (relatively to managers at firms with low exposure) if managers get strong disutility from effort. This happens because incentivizing managers at high exposure firms is more costly. The contract will reduce the cost by decreasing their equity portfolio compensation, generating a negative relation between risk premia and equity-based compensation. When the economy is subject to a series of positive aggregate shocks firms’ profitability will increase. Consequently, managers’ compensations will increase (since they are rewarded for high profits). In the model the cost to incentivize managers increases with their income level (income effect). Thus, managers at firms with low exposure to aggregate risk are more difficult to incentivize, since the managers in this type of firms have, ex-ante, higher longterm compensation than managers at high exposure firms. If the increase in compensation is high enough it will render the managers too costly to be incentivized. Thus, low exposure firms will be better-off replacing them, generating a negative relation between forced turnover and exposure to aggregate risk. Also, in the model aggregate turnover is procyclical. Since firms have a positive exposure to aggregate risk, for all firms it is more expensive to incentivize incumbent CEOs during booms. The better the state of the economy is, the harder it is to incentivize the incumbent CEO. Thus, during booms a high fraction of firms will replace their CEOs. Empirically, the current paper extends in key aspects previous works that study the relations of aggregate risk with compensation and forced turnover. First, I use a long sample that includes booms and recessions that allows a better understanding of the effects of firms’ exposure to aggregate risk. Second, following the asset pricing literature, aggregate risk is measured using the Fama and French three factor model and the Carhart four factor model. Third, to calculate the aggregate and idiosyncratic components of returns, I use daily returns for the previous fiscal year. Using this empirical approach I find a stronger relation between firms’ exposure to aggregate risk and compensation. In the current sample the relation is strongly negative for all managers and not a subsample like in previous works. For turnover, I find similar results than previous literature but stronger.

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This paper relates to the dynamic agency literature. DeMarzo and Sannikov (2006) study the optimal dynamic contract implemented using the firm’s capital structure. DeMarzo and Fishman (2007) derive the investment, capital structure and dividend dynamics under agency conflicts. He (2009) finds the optimal compensation of the manager when the firm’s size follows a geometric Brownian process. Biais, Mariotti, Rochet, and Villeneuve (2010) study the optimal contract when the risk-neutral manager has limited liability and need to exert effort to reduce the probability of disaster shocks. He (2011) studies the optimal dynamic compensation of the CEO and the optimal capital structure of the firm. Edmans and Gabaix (2011) develop a framework that allows closed-form solutions of dynamic agency models. Edmans, Gabaix, Sadzik, and Sannikov (2012) and He (2012) study the optimal compensation of a CEO when he can privately save. Zhu (2012) studies a dynamic contract when the agent optimally shirks under certain circumstances. Szydlowski (2014) studies the optimal contract when the agent needs to allocate effort between different risky projects. Varas (2014) studies a dual moral hazard model with unobservable effort and imperfectly observable project’s quality. Nikolov and Schmid (2012) estimate a dynamic agency model to quantify the effects of agency conflicts. Inderst and Mueller (2010), Spear and Wang (2005), Sannikov (2008), Wang (2011), and Garrett and Pavan (2012) study the effects of firing policy on firm’s value and the agent’s compensation. DeMarzo, Fishman, He, and Wang (2012), Piskorski and Tchistyi (2010), and Hoffmann and Pfeil (2010) show how the agent’s compensation is affected by aggregate shocks that are related to future profitability of the project but are not under the control of the agent. Axelson and Baliga (2009) also study the circumstances under which the compensation of the CEO should depend on variables out of his control. Eisfeldt and Rampini (2008) find that aggregate turnover is procyclical. Lustig, Syverson, and Van Nieuwerburgh (2011) study the effects of technological changes on the cross-section of CEOs’ compensation. Ai and Li (2014) study the compensation of managers and firms’ investment decision in a neoclassical investment model when there is limited commitment on contracts. Ai, Kiku, and Li (2013);

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Ai and Li (2012) study firms’ investment policies and the compensation of managers in general equilibrium models with two-sided limited commitment model and moral hazard, respectively. In general, the current paper belongs to the literature that studies the effects of agency conflicts on firms’ decisions. In a dynamic moral hazard model Clementi, Cooley, and Di Giannatale (2010) study the drivers of firm’s decline. Quadrini (2004) studies the liquidation and investment dynamics of firms in a dynamic moral hazard framework, with renegotiationproof contracts. Albuquerque and Hopenhayn (2004) and Schmid (2012) study endogenous borrowing constraints under limited commitment, while Clementi and Hopenhayn (2006) study them under moral hazard. Li, Whited, and Wu (2014), Rampini and Viswanathan (2010), and Rampini and Viswanathan (2013) study the effects of collateral constraints on optimal leverage and taxes, risk management, and capital structure, respectively. Bolton, Wang, and Yang (2014) study the optimal contract between a risk-averse entrepreneur and a risk-neutral investor under limited commitment with inalienable risky human capital. Zhang (2014) study the optimal wage contract between the firm and its workers. Also, this paper is related to dynamic models that study managers’ compensation and turnover, Taylor (2010) studies firms’ firing policy when the board of directors learns about the ability of the manager and firing is costly. Taylor (2013) studies wage dynamics when the board of directors learns about the ability of the CEO. Empirically, this paper is close to several strands of literature. This paper is related to the relative performance evaluation literature (Murphy (1985); Gibbons and Murphy (1990); Aggarwal and Samwick (1999a,b); Murphy (1999); Himmelberg and Hubbard (2000)). Also, the paper is linked with studies that find a relation between compensation structure and firms’ characteristics (Gopalan, Milbourn, Song, and Thakor (2013)). Further, the paper is related to the turnover literature (Jenter and Kanaan (2014); Kaplan and Minton (2012); Gao, Harford, and Li (2012); Peters and Wagner (2014)). This paper is linked to the asset pricing literature that studies the effects of aggregate risk

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on firms’ decisions. Zhang (2005), Carlson, Fisher, and Giammarino (2004), and Bai, Hou, Kung, and Zhang (2013) study the effects on firms’ investment decisions. Bhamra, Kuehn, and Strebulaev (2010) analyze the effects on firms’ capital structure decisions. Finally, this paper is related to Tallarini Jr (2000), which highlights the importance of accounting for asset pricing data while understanding the effects of business cycle fluctuations. The paper is organized as follows. Section 2 presents the model and calibration. Section 3 presents the empirical strategy and data. Section 4 discusses the results for the data and the model. Finally, section 5 concludes. The Appendices describe in detail the data and calculations of the different types of compensations, together with the model’s solution procedure and normalization.

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Model

The model consists of heterogeneous firms and a risk-averse infinite lived representative shareholder. The production technology requires labor, i.e. effort, to produce. The production technology is subjected to idiosyncratic and aggregate shocks. The representative shareholder cannot operate the production technology and hires managers to do so (one for each firm). Managers are risk-averse and receive utility from consumption and disutility from effort. Effort is unobservable and managers need to be incentivized to exert effort. Each manager and the representative shareholder enter in a long-term contract. The contract defines CEO’s consumption, effort, and next period life-time utility level. Firms take the stochastic discount factor as given when taking production decisions. The stochastic discount factor is derived from the representative shareholder’s preferences.

2.1

CEO’s problem

The executive’s life-time utility Wt is

6

Wt “ Et

« 8 ÿ

ff δ i´t upHt q ´ νpzt q ,

(1)

i“t

where upHt q is the per-period utility over consumption Ht , νpzt q is the per-period disutility of effort, and δ is the subjective discount factor of the CEO. The executive per-period utility preference is of the CRRA form:

upHt q “

Ht1´σ , 1´σ

(2)

where σ is the reciprocal of the elasticity of intertemporal substitution. The functional form for the disutility of effort is:

1´σ  νpzt q “ ζXt´1 zt ,

(3)

where ζ is a parameter that scales the marginal cost of effort,  is the effort curvature, 1´σ and Xt´1 is scaling the effort so it does not become negligible along the balance growth

path.

2.2

Representative shareholder’s preferences

The representative shareholder has Epstein-Zin preferences over the aggregate consumption Ct stream ! ) θ 1´1{ψ 1´γ θ1 1´γ ` βEt rUt`1 s Ut “ p1 ´ βqCt

(4)

where β is the subjective discount factor, , ψ is the elasticity of intertemporal substitution, γ is the risk aversion, θ ” p1 ´ γq{p1 ´ 1{ψq is defined for convenience. The stochastic discount factor is

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1

˜ Mt`1 “ β

Ct`1 Ct

¸ ψ1 ˜

1´γ Ut`1 1´γ Et rUt`1 s

´γ ¸ ψ1´γ

(5)

Following Bansal and Yaron (2004), the log consumption growth (∆ct “ log pCt {Ct´1 q) is exogenously specified as: ˆ log

Ct Ct´1

˙ “ g¯ ` gct ,

(6)

where gct is an AR(1) process:

gct “ ρc gct´1 ` σc εct ,

(7)

where ρc is the persistence, σc is the volatility, and εct is a standard normally distributed random variable.

2.3

Representative shareholder’s problem

Equation 8 shows that firm’s profit depends on an aggregate component Xit , an idiosyncratic component ξpzt q and CEO’s current consumption Ht .

πit “ ξit pzit q Xit ´ Hit .

(8)

The aggregate risk component exposes the firm to consumption growth risk: ˆ log

Xit Xit´1

˙ “ g¯ ` φi gct .

(9)

As in Bansal, Dittmar, and Lundblad (2005) firm’s exposure heterogeneity is given by φi , a higher φi increases the exposure to consumption growth. The probability distribution of the idiosyncratic risk depends on the effort of the executive. The higher the effort exerted by the executive the higher the probability of positive idiosyncratic shocks. The executive’s 8

consumption, as well as his effort, are endogenous and depend on the optimal contract between the firm and the executive. Following Spear and Wang (2005) and Wang (2011), the firm can fire the CEO after paying a cost C and can hire a new one. The representative shareholder has to compare between the value of the firm retaining the current CEO (Vtr ) and the value of the firm replacing the CEO (Vtf ), the value of the firm Vt is given by:

Vt “ maxtVtr , Vtf u,

(10)

the value of the firm retaining the CEO Vtr is given by:

Vtr “

max

zt ,Ht ,Wt`1

Et rξ pzt q Xt ´ Ht ` Mt`1 Vt`1 s ,

(11)

where W is the promised life-time utility to the CEO, and Vt`1 is the value of the firm next period. The value of the firm when it fires the CEO Vtf is given by:

x , .q|W x ą W0 u ´ CpW q. Vtf pW, .q “ maxtVtr pW

(12)

x W

Equation 12 shows that the value of the firm when it fires the CEO has two terms. The first term is the value of the firm under the new management. The firm hires the new CEO and promises him a utility level that maximizes the value of the firm Vtr .3 The second term is the cost of firing the current CEO, which is the cost of the severance package that has to be paid to the CEO. The payment is the amount that is the certainty equivalent, in consumption units, of the life-time utility level, W , promised to the CEO. 3

Implicitly this assumption means that a new CEO is hired and retained for at least one period.

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2.4

Timing

Figure 1 shows the timing of events within a period. The aggregate shock is known prior to the beginning of the period. Following Sannikov (2008) and Sannikov (2012) effort and consumption are executed at the beginning of the period. The idiosyncratic shock is realized in the middle of the period after effort is exerted. Value of the firm V pWi,t , Ct q is calculated Ct

Firm specific shock

Wi,t

Ct`1 Wi,t`1 pξi,t , Ct`1 q

ξi,t pzi,t q

[Hi,t , zi,t ]

t`1

t Figure 1: Timing of events inside a period

2.5

Optimal dynamic contract

In the model all the state variables and policy functions can be observed by the representative shareholder, except for the effort level exerted by the CEO. Since effort is unobservable, this causes a moral hazard problem. The contract has to incentivize the CEO to exert effort and not to deviate from the contract. Following Spear and Srivastava (1987) the optimal contract can be expressed recursively if the state space is extended to include the promised utility to the CEO as a new state variable. Thus, the state variables of the model are aggregate consumption (C) and CEO’s promised utility (W ). The optimal contract problem with moral hazard, written in a recursive form, is

˜ V r pWt , Ct q “

max

zt ,Ht ,Wt`1

ÿ

¸

ppξ|zt q ξ pzt q Xt ´ Ht `

ÿ

QpCt , Ct`1 q rM V pWt`1 , Ct`1 qs ,

C

ξ

(13) subject to the incentive compatibility constraints (IC):

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˜ ÿ

ppξ|zt q

ξ

˜ ÿ

ppξ|ˆ zt q

ξ

ÿ Ht1´σ 1´σ  zt ` δ QpCt , Ct`1 qWt`1 ´ ζXt´1 1´σ C

¸ ě

¸ ÿ Ht1´σ 1´σ  ´ ζXt´1 zˆt ` δ QpCt , Ct`1 qWt`1 @z, zˆ 1´σ C

(14)

and the promise keeping constraint (PK): ˜ Wt “

ÿ ξ

ppξ|zt q

¸ ÿ Ht1´σ 1´σ  ´ ζXt´1 zt ` δ QpCt , Ct`1 qWt`1 pξt , Ct`1 q . 1´σ C

(15)

The IC constraint (Equation 14) is needed since the CEO effort is unobservable. The IC says that the promised utility offered by the contract, given the state of the economy, suggested effort z, and CEO’s consumption, has to be greater or equal than the life-time utility obtained by exerting a different effort level zˆ. Thus, the contract incentivizes the CEO to exert the optimal effort by giving him a life-time utility level that it is at least equal to any other. The promise keeping constraint says that the utility promised to the CEO has to be delivered. The promise keeping constrain is needed to be able to write the problem in a recursive form.

3 3.1

Empirical methodology Data

The data is obtained from different sources. Firms’ information is from COMPUSTAT, executive information is from EXECUCOMP, and returns information is from CRSP. CEO compensation is divided into 2 categories: cash compensation and equity portfolio compensation. Cash compensation represents cash payments received by the executive in the current fiscal year. Equity portfolio compensation is the market value of compensations that the executive will receive in the future. Total compensation is defined as cash compensation plus 11

equity portfolio compensation. Appendix B includes a detailed definition of the different types of compensations. The market value of future compensation depends on the market value of the firm’s shares owned by the executive, and the market value of the stock options granted to the executive. The most demanding task is to calculate the market value of the different stock options. Stock options differ in their maturity, vested/unvested condition, and vesting period. In the literature, different ways are used to calculate the value of the stock options. In the current paper I follow Coles, Daniel, and Naveen (2006). This method also takes into account different maturities, vesting periods, and vested/unvested conditions. Appendix B explains in detail the different methods. The firm’s aggregate risk is measured in two different ways. The Fama and French three factor model, and the Carhart four factor model are used. The aggregate exposure is calculated using one year of daily returns for the preceding fiscal year. Only firms with more than six months of stock returns are used.

3.2

Data regressions

Following Aggarwal and Samwick (1999b), and Garvey and Milbourn (2003) the executive’s compensation is regressed on the change in shareholder’s wealth, the interactions between the change in shareholder’s wealth and the variance of stock returns (decomposed into aggregate and idiosyncratic components), and a set of controls:

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2 qit Cashit “ α0 ` η ∆ShrWealthit ` α1 ∆ShrWealthit ˆ CDFpσAgg 2 ` α2 ∆ShrWealthit ˆ CDFpσIdio qit ` γ 1 Xit ` εC,it ,

(16)

2 ∆Equityit “ β0 ` ν ∆ShrWealthit ` β1 ∆ShrWealthit ˆ CDFpσAgg qit 2 ` β2 ∆ShrWealthit ˆ CDFpσIdio qit ` ρ1 Xit ` εE,it ,

(17)

2 ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` ϕ1 ∆ShrWealthit ˆ CDFpσAgg qit 2 qit ` ι1 Xit ` εT,it , ` ϕ2 ∆ShrWealthit ˆ CDFpσIdio

(18)

where CDF stands for cumulative density function, and Xit is the set of controls. The controls are the interaction between the change in shareholders’ wealth and the CDF of Tobin’s Q, CDF of Tobin’s Q, and the CDFs of the firm’s aggregate and idiosyncratic variances. Instead of directly using the aggregate and idiosyncratic variance I use the cumulative distribution function of the variables, as in Aggarwal and Samwick (1999b). The CDF is used since it allows to directly calculate the elasticity of the executive’s compensation to a change in the stock returns variance. Firm’s aggregate variance and idiosyncratic variance are measured in dollar terms. In multi-factor models it is also important to analyze the relative contribution of each of the factors. For this purpose, firm’s aggregate variance is decomposed into the contribution of each of the factors. Regressions 16-18 are substituted by

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Cashit “ α0 ` η ∆ShrWealthit `

N ÿ

αj ∆ShrWealthit ˆ CDFpσf2j qit

j“1 2 qit ` γ 1 Xit ` εC,it , ` αN `1 ∆ShrWealthit ˆ CDFpσIdio

∆Equityit “ β0 ` ν ∆ShrWealthit `

N ÿ

βj ∆ShrWealthit ˆ CDFpσf2j qit

j“1 2 ` βN `1 ∆ShrWealthit ˆ CDFpσIdio qit ` ρ1 Xit ` εE,it ,

∆Totalit “ ϕ0 ` δ ∆ShrWealthit `

N ÿ

ϕj ∆ShrWealthit ˆ CDFpσf2j qit

j“1 2 ` ϕN `1 ∆ShrWealthit ˆ CDFpσIdio qit ` ι1 Xit ` εT,it ,

where tfj uN j“1 are the factors.

3.3

Turnover probability and firm’s exposure to aggregate risk

I follow Bushman, Dai, and Wang (2010) to study the effects of firm’s exposure to aggregate risk on forced turnover probability. I extend their study in two important ways. First, I extend their sample to include the financial crisis (1993-2010). Second, to calculate the aggregate risk of the firm, I use the Fama and French 3 factor model and the Carhart 4 factor model, instead of only the market return. Empirically, the Fama and French and the Carhart models fit returns better than just using the market return as regressor. Following Bushman, Dai, and Wang (2010) I use a two step-approach. In the first step firm’s stock return is regressed on a factor model (Fama and French three factor model or Carhart four factor model). The first regression is calculated using daily data for the previous fiscal year. Thus, the process calculates different exposure for each year. In the second step a forced turnover dummy is regressed on the firm’s aggregate and idiosyncratic risks, which are, respectively, the standard deviation of the predicted and the error term of 14

the first step regression:

P rpForcedit q “ F pα ` γσAggit ` ρσIdioit ` ς 1 Xit ` it q,

(19)

where Forcedit is a dummy variable that measures forced turnovers and is equal to one when the turnover is forced and zero otherwise, σAggit is the firm’s aggregate risk, σIdioit is the idiosyncratic risk, and Xit is a set of controls. In Equation 19 the probability is calculated using a logit regression. To classify turnovers as forced or voluntary I follow Parrino (1997).4 The data is winsorized at the 1th and 99th percentiles. Variables denominated in dollars are measured in real terms; they are deflated using the CPI.

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Results

4.1

CEO compensation

The relation between aggregate risk and CEO compensation is explored here. Table 1 shows the result for the Fama and French 3 factor model. Column (1) shows that in the data there is positive relation between pay-performance sensitivity to aggregate risk 2 (∆W ealth ˆ CDFpσAgg q) and cash compensation, although the point estimate is not sta-

tistically significant. In contrast, column (2) shows that there is a statistically significant negative relation between the change in equity portfolio compensation and firm’s exposure to aggregate risk. For total compensation (column (3)) there is also a negative relation. To study the robustness of this result Tables 2 and 3 present specifications with several controls. Table 2 shows specifications with the interaction between change in shareholders’ wealth and the CDF of Tobin’s Q, CDF of Tobin’s Q, the CDFs of firm’s aggregate and idiosyncratic variances. For equity portfolio and total compensation the results are con4

I thank Kai Li for providing me the data

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sistent along the different specifications. The pay-performance sensitivity to aggregate risk 2 (∆W ealthˆCDFpσAgg q) is negative and stable; it slightly decreases in magnitude when more 2 controls are included. For columns (8) and (9) the effect of firm’s aggregate risk (CDFpσAgg q)

is negative for equity portfolio and total compensation. The results suggest a strong negative relation between aggregate risk and equity-based compensation. For cash compensation, 2 the results are not stable. For columns (1) and (4) ∆W ealth ˆ CDFpσAgg q is positive and

statistically significant. For column (7) the coefficient is negative and statistically insignifi2 cant, but the coefficient for CDFpσAgg q is positive and statistically significant. This suggests

that there is a weak positive link between cash compensation needs and firm’s exposure to aggregate risk. Table 3 includes the expected return, in dollars, as explanatory variable (BenchpAggq). A negative coefficient indicates that the firm is reducing aggregate risk from compensation. The data shows that in fact firms are decreasing the exposure of CEOs to aggregate risk. The results are stable and in line with the other specifications. To analyze in more detail the importance of each risk factor Table 4 shows the results specifying the contribution of each factor. The estimates for the market factor and the SMB factor are negative; the market factor is the only statistically significant. For the HML factor the coefficient is positive and statistically significant. Economically, the risk market factor is, in magnitude, the most important of the three factors. This suggests that the pay-performance sensitivity decreases for the market and the SMB factors. In Table 5 I run several specifications with different controls. Table 5 shows that the inter2 actions of the change in shareholders’ wealth with the market factor (∆W ealthˆCDFpσRM q) 2 and the SMB factor (∆W ealth ˆ CDFpσSize q) are negative for equity portfolio compensation

and total compensation. Only the interaction with the market factor is statistically significant. When I include the direct effect of each of the factors (column (8)) I find that for the market factor and the SMB factor the coefficients are negative and statistically significant. In short, there is a strong negative relation between equity-based compensation and the

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aggregate risk generated by each of the factors, with the exception of the HML factor. The current results are in line with the previous literature (Garvey and Milbourn (2003), and Jin (2002) ). Current results are statistically stronger since I use a longer series that takes into account the effects of the great recession, and better reflects the effects of aggregate risk on the compensation of managers.

4.2

Turnover

The relation between aggregate risk and turnover is explored here. Table 6 shows the effects of aggregate risk on CEOs’ turnover. The probability decreases with firm’s exposure to aggregate risk and increases with idiosyncratic risk. The higher the exposure to aggregate risk the lower is the probability of turnover since they have less equity portfolio compensation. Thus, firms with low exposure have a higher turnover rate. The results presented here are in line with the results of Bushman, Dai, and Wang (2010). Current results are statistically stronger, since, as in the previous case, a longer sample better captures the effects of good and bad times.

4.3

Model

In this section simulations from the model are explored. A panel of 5,000 firms is simulated for 520 periods; the first 400 periods are dropped to eliminate the influence of the initial distribution on the results. Table 7 presents the monthly calibration. Panel A presents the preference parameters for the representative shareholder. The subjective discount factor β is set to 0.99, the risk aversion γ is set to 5, and the elasticity of intertemporal substitution ψ is set to 2. The values are in line with the long-run risks literature. Panel B reports the preference parameters of the managers. The subjective discount factor δ is set to 0.95. The risk aversion parameter σ, and the effort curvature  are fixed at 1.2 and 2, respectively. These parameters are calibrated to standard values in the dynamic 17

agency models (Moll, Townsend, and Zhorin (2014); Karaivanov and Townsend (2014)). Finally, the marginal cost of effort parameter ζ is set to 2.5. The parameter is calibrated to help match the ratio of expected cash compensation to expected equity compensation (reported in Table 8 ). Panel C reports the parameters for the aggregate consumption process. The average consumption growth rate g¯ is set to 0.019{12, the persistence of consumption growth ρg and the volatility of consumption growth σg are fixed at 0.92 and 0.0015, respectively. These values are standard in the long-run risks literature. They help to match the value premium (reported in Table 8 ). Table 9 presents the results of the influence of aggregate risk on executive compensation. The model is able to replicate the data results. In the model, managers’ compensation structures will differ for firms with different exposure to aggregate risk, because firms’ riskiness will differ. A firm with high exposure to aggregate risk has more volatile revenues than a low exposure firm. Its manager would also have a high exposure to incentivize him. It is more costly to incentivize the manager in high exposure firms; the contract will reduce the cost by decreasing his equity portfolio compensation (relative to low exposure firms). The model is also able to replicate the relation between turnover and aggregate risk, as shown in Table 10. When the economy is subject to a series of positive aggregate shocks the firms’ profitability and managers’ total compensation will increase. In the model the cost to incentivize managers increases in their income level (income effect). Thus, managers at firms with low exposure to aggregate risk are more costly to incentivize, since the managers in this type of firms have, ex-ante, higher equity-based compensation than managers at high exposure firms. Thus, low exposure firms are better-off firing them, generating a negative relation between turnover and exposure to aggregate risk. The model can replicate the procyclicality of aggregate turnover. Eisfeldt and Rampini (2008) find that the correlation between aggregate turnover and output growth is 0.54; aggregate turnover in the model has a correlation with aggregate consumption growth of

18

0.828. In the model, all types of firms are positively exposed to aggregate risk. As explained before, during booms firms need to increase total compensation to incentivize the managers. When the aggregate shock is positive and large enough, a big fraction of firms will fire the incumbents CEOs because they are too expensive. Table 11 presents comparative statistics for cash compensation, equity-based compensation and turnover. In Column 3, the subjective discount factor of the managers is lowered from the benchmark calibration of 0.95 to 0.9. A lower discount factor makes the manager more impatient and he prefers consumption now rather than later. This can be seen in the relation between cash compensation and risk premia, the sensitivity is higher than on the benchmark case. Furthermore, for the equity portfolio compensation the parameter is lower (in absolute value) than in the benchmark case, decreasing the sensitivity to equity portfolio compensation. The probability of turnover decreases less with an increase in exposure to aggregate risk, this is in line with the higher sensitivity to cash payment and lower sensitivity to equity portfolio compensation. In column 4, the representative shareholder has CRRA preferences. In this case the risk averse shareholder does not care about the uncertainty of long term growth prospects. This can be seen in the low sensitivity of equity compensation to firm’s exposure to aggregate risk. Cash compensation sensitivity is similar between the CRRA case and the benchmark case; this means that the sensitivity for short term compensation is similar in both cases. This also can be seen in the sensitivity of the turnover probability to aggregate risk which decreases less with an increase in exposure to aggregate risk. In column 5, the representative shareholder is risk neutral. The representative shareholder has no longer a strong negative sensitivity to recessions (marginal utility is constant). Thus, the incentives problem is, in this case, much less costly for her. Therefore, managers at high exposure firms can be incentivized using more long-term compensation and less short-term compensation. This is reflected in the positive sensitivity to equity portfolio compensation and the negative sensitivity to cash compensation. Now, managers at high exposure firms

19

have more equity portfolio compensation than managers at low exposure firms, generating a positive relation between turnover and exposure to aggregate risk. In column 6, the risk aversion parameter of the manager is increased from 1.2 to 2. In this case the manager is more risk-averse and also his elasticity of intertemporal substitution is smaller (from 0.8 to 0.5). The manager prefers a smoother consumption path; this can be seen in the low sensitivity of equity compensation to risk premia. This means that equity compensation barely changes when there is a change in exposure to aggregate risk. Cash compensation changes to keep the manager incentivized since equity portfolio compensation is not changing. In contrast to the base case, turnover probability increases with firm’s exposure to aggregate risk. In this case managers at firms with high exposure to aggregate risk have similar levels of equity portfolio compensation than managers at low exposure firms; this means that during expansions managers at high exposure firms have higher levels of equity portfolio compensation. Thus, they are the first to be fired during expansion, generating a positive relation between exposure to aggregate risk and turnover. In column 7, the marginal cost of effort parameter is decreased from 2.5 to 0.5. In this case the effort exerted by the manager is less costly for him, and he is easier to be incentivized. This is reflected in the negative sensitivity to cash compensation and the positive sensitivity to equity-based compensation. In this case, it is much less costly for the representative shareholder that the incentives problem is more severe during recessions. Therefore, the representative shareholder can increase the equity portfolio compensation for managers at firms with high exposure (relatively to managers at low exposure firms) to incentivize them without suffering the negative consequences during downturns. Turnover decreases more in this case than in the benchmark; this is due to the negative sensitivity to cash compensation, which generates that total compensation is negatively related to aggregate risk exposure.

20

4.4

Robustness

In this section the data regressions are calculated using the Carhart four factor model to calculate the aggregate component of returns. Tables 12, 13, and 14 replicate the results presented in Tables 1, 2, and 3, respectively. The negative relation between firm’s exposure to aggregate risk and equity-based compensation is stronger economically and statistically. Also, the positive relation between cash compensation and firm’s exposure to aggregate risk is stronger. In the case of turnover Table 15 replicates the results in Table 6. The results are stronger economically and statistically.

5

Conclusion

This paper relates firms’ risk premia with the compensation structure and firing policy of managers, by studying a dynamic moral hazard model with aggregate risk. When managers receive high levels of disutility from effort and shareholders are averse to uncertainty about long-term growth prospects, firms will link compensation to realized cash flows to be able to incentivize the managers. Managers in firms with high exposure will favor less long-term compensation. Consequently, the model explains the negative relation between aggregate risk and equity-based compensation. The model can also explain the negative relation between risk premia and forced turnover, and the procyclicality of turnover at the aggregate level. In short, this paper highlights the importance of risk premia in understanding the dynamics of CEO contracts.

21

Appendix A Data Implementation A.1 Data definition Executive compensation data is from EXECUCOMP, firms’ balance sheet data is from COMPUSTAT, stock returns data is from CRSP. • ALLOTHPD: The portion of “All Other Compensation” that is paid or payable in cash during the indicated fiscal year. The indicated amount of a portion of the item “All Other Total”. • ALLOTHTOT: This is the amount listed under“All Other Compensation” in the Summary Compensation Table. • Bonus: The dollar value of a bonus earned by the named executive officer during the fiscal year. • DIVYIELD: The Dividends per Share by Ex-Date divided by Close Price for the fiscal year. This quotient is then multiplied by 100. • OPT UNEX EXER NUM: The aggregate number of unexercised options held by the executive at fiscal year end that were vested. • OPT UNEX EXER EST VAL: Value of in-the-money vested options at fiscal year end as reported by the company (pre-2006). • OPT UNEX UNEXER NUM: The aggregate number of unexercised options held by the executive at fiscal year end that were not yet vested. • OPT UNEX UNEXER EST VAL: Value of in-the-money unvested options at fiscal year end as reported by the company (pre-2006). • OPTION AWARDS NUM: Total number of options awarded during the year as detailed in the Plan Based Awards table. 22

• OPTION AWARDS RPT VALUE: The aggregate value of all options granted to the executive during the year as valued by the company. • OPTION AWARDS FV : Fair value of all options awarded during the year as detailed in the Plan Based Awards table. Valuation is based upon the grant-date fair value as detailed in FAS 123R. • OPT EXER NUM: Number of options exercised by the executive during the year. • OTHANN: The dollar value of other annual compensation not properly categorized as salary or bonus. • PRCCF: The Close Price of the company’s stock for the fiscal year. • RSTKGRNT: The value of restricted stock granted during the year (determined as of the date of the grant). • Salary: The dollar value of the base salary earned by the named executive officer during the fiscal year. • SHROWN EXCL OPTS: Shares owned by the executive, excluding options that are exercisable or will become exercisable within 60 days. Share ownership is generally reported as of a date between the fiscal year end and proxy publication. • STOCK AWARDS FV: Fair value of all stock awards during the year as detailed in the Plan Based Awards table. Valuation is based upon the grant-date fair value as detailed in FAS 123R. • STOCK UNVEST NUM: Aggregate shares of restricted stock held by the executive that had not yet vested as of fiscal year end.

23

Appendix B Compensation B.1 Cash Compensation • Salary. • Bonus. • Net revenue from trade in stock. • Dividends • Long-term incentives payouts (ALLOTHTOT-ALLOTHPD). • Others (ALLOTHPD+OTHANN)

B.1.1 Net revenue from trade in stock The net revenue from trading (Net Rev) is calculated as:

Net Rev “ maxtNet Sold ¨ PRCCF ´ CEX, 0u, where Net Sold is the net number of shares sold (including shares received by exercising stock options), PRCCF is the price at the end of the fiscal year, and CEX is the cost of exercising stock options. Net Sold and CEX are unknown. First, CEX is calculated from Equation B.1. It shows that the cost of exercising the stock options is equal to the number of options exercised (OPT EXER NUM) times the strike price (STRIKE)

CEX “ OPT EXER NUM ˆ STRIKE.

(B.1)

The strike price is unknown. To find the strike price Clementi and Cooley (2009) assume that the options are exercised at the maximum stock price during the fiscal year. The strike

24

price is found by solving:

OPT EXER VAL “ pMAX PRICE ´ STRIKEq OPT EXER NUM,

(B.2)

where OPT EXER VAL is the value of options exercised and MAX PRICE is the maximum stock price. Second, the net number of shares sold can be calculated from the law of motion for the numbers of shares own by the executive (SHROWN):

SHROWNt “ SHROWNt´1 ` VESTt ` OPT EXER NUMt ´ Net Sold.

(B.3)

Equation B.3 shows that the number of shares own today (SHROWNt ), is equal to the number of shares own last period (SHROWNt´1 ) plus the number of restricted shares that vested (VESTt ) plus the number of shares received by exercising stock options (OPT EXER NUMt ) minus the net number of shares sold (Net Sold). Thus, the net value of shares sold is:

Net Sold “ SHROWNt´1 ´ SHROWNt ` VESTt ` OPT EXER NUMt .

The number of stocks that vested VESTt is unknown. It can be obtained from the law of motion for the total number of restricted stocks (STOCK UNVEST NUM):

STOCK UNVEST NUMt “ STOCK UNVEST NUMt´1 ` GRNTt ´ VESTt ,

where the number of granted restricted stocks GRNTt can be calculated as the value of restricted stocks granted during the current fiscal year divided by the closing price for the fiscal year:

25

GRNTt “

RST KGRN T . P RCCF

B.2 Equity Portfolio Compensation Equity-based compensation is the summation of: • Executive’s shares value. • Executive’s options value. The executive’s shares value is:

S “ SHROWNt ¨ PRCCFt . B.2.1 Options To calculate the options value there are different methods. The present paper follows Core and Guay (2002); for a detailed explanation of the method see Coles, Daniel, and Naveen (2013). The options portfolio is divided in three different groups: options granted during the current fiscal year (assumed unvested), unvested options and vested options. Options values, for the three different portfolios, are calculated at the end of the fiscal year using the Black and Scholes formula. For the options granted during the current fiscal year is possible to obtain: the strike price (EXPRIC), expiration (EXDATE), and number of options (OPTION AWARDS NUM) from EXECUCOMP. The unvested options portfolio excludes current option grants. Thus, the net number of unvested options (NET OPT UNEX UNEXER NUM) is calculated as:

26

NET OPT UNEX UNEXER NUMt “ maxtOPT UNEX UNEXER NUMt ´ OPTION AWARDS NUMt , 0u.

(B.4)

Equation B.4 states that if the difference between unvested options and current option grants is negative then the net number of unvested options is zero. The time to maturity is calculated as the average time to maturity for current grants minus 1 year. If the number of current grants is zero, the maturity is set to nine years. The exercise price is obtained as if the options were to be exercised immediately, i.e., the value of the options today is equal to the difference between the current spot price and the strike price times the number of options:

NET OPT UNEX UNEXER VALt “ pPRCCFt ´STRIKEt q¨NET OPT UNEX UNEXER NUMt .

Thus, the strike price can be calculated as:

STRIKE UNVESTt “ PRCCFt ´

NET OPT UNEX UNEXER VALt . NET OPT UNEX UNEXER NUMt

For vested options the time to maturity is calculated as the time to maturity for unvested options minus 3 year. The number of vested options in the portfolio is equal to the total number of vested options minus the net number of unvested options (only if it is negative):

NET OPT UNEX EXER NUMt “ OPT UNEX EXER NUMt ` maxt´pOPT UNEX UNEXER NUMt ´ OPTION AWARDS NUMt q, 0u.

The exercise price is also obtained as if the options were to be exercised immediately:

27

STRIKE VESTt “ PRCCFt ´

NET OPT UNEX EXER VALt . NET OPT UNEX EXER NUMt

The Black and Scholes formula for options written on dividend paying stock, is given by:

optt “ Se´qT N pd1 q ´ Xe´rT N pd2 q, where S is the spot price of the underlying asset, q is the dividend yield, X is the strike price, T is the time to maturity, and N is the standard normal cumulative distribution function. d1 and d2 are given by: ` ˘ ` r ´ q ` 12 σ 2 T ? , d1 “ σ T ? d2 “ d1 ´ σ T , log

`S˘ X

where σ denotes the stock return volatility. q is calculated using the DIVYIELD variable from EXECUCOMP, r is obtained from the Federal Reserve, specifically, the Constant Maturity Treasuries (annual frequency). The interest rate used corresponds to the CMT with the same maturity as the option.

5

Also, S

is the stock price at the end of the fiscal year P RCCF .

Appendix C Normalization Since the model is non-stationary it has to be normalized to be able to solve it. Equation 13 is normalized by Xt´1 : ˜ „ ¸ ÿ ÿ Xt V pWt , Xt q Xt Ht V pWt`1 , Xt`1 q “ max ppξ|zt q ξ pzt q ´ ` QpCt , Ct`1 q M , zt ,Ht ,Wt`1 Xt´1 Xt´1 Xt´1 Xt´1 Xt C ξ (C.5)

getting: 5

i.e. if the maturity of the option is one year, the interest rate used is the one year CMT yield. For options with maturity greater or equal to 10 years, the ten year yield is used.

28

˜ Vpt “

ÿ

max

p t ,W ˆ t`1 z t ,H ξ

¸

p t ` eg¯`φi gct ppξ|zt q ξ pzt q eg¯`φi gct ´ H

ÿ

”

ı

Qp∆ct , ∆ct`1 q M p∆ct`1 qVpt`1

,

∆c

(C.6) 1´σ The IC (Equation 14) and the PK (Equation 14) constraints are normalized by Xt´1 :

¨´ ÿ

˚ ppξ|zt q ˝ ¨´ ˚ ppξ|p zt q ˝

ξ

Ht Xt´1

˛

¯1´σ ´ ζzt ` δ

1´σ

ξ

ÿ

Ht Xt´1

Xt ÿ Wt`1 ‹ Qp∆ct , ∆ct`1 q ‚ě Xt´1 ∆c Xt ˛

¯1´σ

1´σ

´ ζ zˆt ` δ

Xt ÿ Wt`1 ‹ Qp∆ct , ∆ct`1 q ‚@z, zˆ Xt´1 ∆c Xt

(C.7)

and the promise keeping constraint (PK):

¨´ ÿ Wt ˚ “ ppξ|zt q ˝ 1´σ Xt´1 ξ

Ht Xt´1

˛

¯1´σ

1´σ

´ ζzt ` δ

Xt ÿ Wt`1 ‹ Qp∆ct , ∆ct`1 q ‚, Xt´1 ∆c Xt

(C.8)

getting:

¸ ÿ xt 1´σ H xt`1 ě ppξ|zt q ´ ζzt ` δep1´σqp¯g`φi gct q Qp∆ct , ∆ct`1 qW 1 ´ σ ∆c ξ ˜ ¸ ÿ ÿ p t1´σ H xt`1 @z, zˆ ppξ|ˆ zt q ´ ζ zˆt ` δep1´σqp¯g`φi gct q Qp∆ct , ∆ct`1 qW 1 ´ σ ∆c ξ ˜

ÿ

(C.9)

and the promise keeping constraint (PK):

˜ xt “ W

ÿ ξ

ppξ|zt q

¸ ÿ p t1´σ H xt`1 , ´ ζzt ` δep1´σqp¯g`φi gct q Qp∆ct , ∆ct`1 qW 1´σ ∆c 29

(C.10)

Appendix D Implementation The model is solved following the method developed by Phelan and Townsend (1991). The method has three steps. First, the model is discretized and re-written in term of lotteries over the policy functions and shocks, which are the new decision variables. Second, the value of the firm is found using value function iteration. Third, at each iteration and at each point of the state space the lotteries are found by solving a linear programming problem. The advantage of this method is twofold. First, by using probabilities it convexifies the constraint set, allowing to solve problems that do not have a convex constraint set. Second, there are highly optimized computational routines to solve linear programming problems with accuracy and speed. The drawback is the curse of dimensionality, it is necessary to understand the characteristic of the model to choose the state variables and policies grids in an optimal manner. In the discretized model the state variables as well as the policy functions can take only a discrete set of values (grids). Let Z, H, W , G, and Ξ be the grids for effort, CEO’s consumption, promised utility, consumption growth 6 , and idiosyncratic shock, respectively. Then, the probabilities are defined over the cartesian products of the grids, given the current state of the economy:

xt q : H ˆ Ξ ˆ Z ˆ W ˆ G Ñ r0, 1s πp.|gct , W

(D.11)

The model expressed in terms of the probabilities πp.q is:

« ÿ

Vpt “ max πp.q

ff

g `φi gct q p¯ p t , ξt , zt , W xt`1 , g p t ` ep¯g`φi gct q Mt`1 Vpt`1 , πpH ´H xt q ξt e c t`1|gct ,W

(D.12)

xt ,ξt , H xt`1 , W zt ,gc t`1

subject to: 6

In the implementation I write the grid in terms of gc instead of ∆c, remember that ∆ct “ g¯ ` gct .

30

«

ÿ

xt “ W

p t ,ξt , H xt`1 , W zt ,gc t`1

ff p t1´σ H p t , ξ, zt , W xt`1 , gc t`1 |gct , W xt q xt`1 , πpH ´ ζzt ` δep1´σqpg¯`φgc,t q W 1´σ

˜ ÿ

p t , ξ, zt , W xt`1 , gc t`1 |gct , W xt q πpH

p t ,ξt , H xt`1 , W zt ,gc t`1

˜ ÿ

p t , ξ, zt , W xt`1 , gc t`1 |gct , W xt q πpH

p t ,ξt , H xt`1 , W zt ,gc t`1

xt 1´σ H xt`1 ´ ζzt ` δep1´σqp¯g`φi gct q W 1´σ

p t1´σ H xt`1 ´ ζ zˆt ` δep1´σqp¯g`φi gct q W 1´σ

(D.13)

¸ ě

¸

@pz, zˆq P Z ˆ Z

(D.14)

p t , ξ, zt , W xt`1 , gc t`1 |gct , W xt q ě 0, πpH

ÿ

(D.15)

p t , ξ, zt , W xt`1 , gc t`1 |gct , W xt q “ 1, πpH

(D.16)

p t ,ξt , H xt`1 , W zt ,gc t`1

ÿ

¯ ¯ p xt`1 , gc t`1 |gct , W xt q “ πpH ¯t , W t , ξt , z

xt`1 W

¨ ¯ zt , gc,t , W xt q ˝ P pξ|¯

˛ ¯ p xt`1 , gc t`1 |gct , W xt q‚Qpgct , gc t`1 q πpH ¯t , W t , ξt , z

ÿ

xt`1 ,gc ξt ,W

t`1

¯ ¯ z¯, H, p @pξ, gc t`1 q P Ξ ˆ Z ˆ H ˆ G.

(D.17)

Equation D.12 is the maximization of the firm’s value. The maximization is over the probabilities. Equations D.13 and D.14 are the promise keeping and incentive compatibility 31

constraints. Equations D.15- D.17 are included to insure that the πs are true probabilities. Equation D.15 states that the probabilities are positive, Equation D.16 states that the sum of the probabilities must be equal to one, Equation D.17 shows that the Bayes’ rule has to hold. To see more clearly the relation between condition probabilities Equation D.17 can be written as:

¯ ¯ ¯ ¯ p xt q “ P pξ¯t |¯ p x p ˜ P pH ¯t , gc t`1 |gct , W zt , H zt , H t , ξt , z t , gct , Wt qP p¯ t |gc,t , Wt qQpgct , gc t`1 q.

(D.18)

In the model the idiosyncratic shock depends only on the effort of the executive (P pξ¯t |¯ zt q “ ¯ p x P pξ¯t |¯ zt , H t , gct , Wt ). Thus, the previous equation can be simplified even further: ¯ ¯ ¯ p xt q “ P pξ¯t |¯ p ˜ P pH ¯t , gc t`1 |gc,t , W zt qP p¯ zt , H t , ξt , z t , |gc,t , Wt qQpgct , gc t`1 q.

(D.19)

It is important to highlight that Equation D.16 shows that effort and consumption are established at the beginning of each period, as in Sannikov (2012). In other words, the consumption received by the executive in the current period does not depend on the value of the current idiosyncratic shock, which is realized in the middle of the period.

32

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Table 1: Data regression: CEO compensation and risk premia (1) (2) Cash Equity ∆W ealth -0.0000886 0.0135˚˚˚ (-1.53) (30.64) 2 ∆W ealth ˆ CDFpσAgg q 0.000168 -0.00720˚˚˚ (1.64) (-9.76) 2 ∆W ealth ˆ CDFpσIdio q -0.0000839 -0.00546˚˚˚ (-0.75) (-7.41) Constant 2.215˚˚˚ -0.579˚˚˚ (401.63) (-11.91) Coperol FE yes yes N 126407 100806

(3) Total 0.0135˚˚˚ (30.58) -0.00721˚˚˚ (-9.76) -0.00547˚˚˚ (-7.43) -0.573˚˚˚ (-11.73) yes 100628

t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01 This table presents data results for different specifications of 3 different regression. Column (1) shows 2 the results of: Cashit “ α0 ` η ∆ShrWealthit ` α1 ∆ShrWealthit ˆ CDFpσAgg qit ` α2 ∆ShrWealthit ˆ 2 CDFpσIdio qit ` εC,it ; it regresses cash compensation on the change in shareholders’ wealth, the interaction between shareholders’ wealth and firm’s aggregate variance, and the interaction between shareholders’ wealth and idiosyncratic variance. Firm’s aggregate variance is calculated using the Fama and French 3 factor model. 2 qit ` Column (2) shows the results for ∆Equityit “ β0 ` ν ∆ShrWealthit ` β1 ∆ShrWealthit ˆ CDFpσAgg 2 β2 ∆ShrWealthit ˆ CDFpσIdio qit ` εE,it ; it regresses equity portfolio compensation on the same exogenous variables as the previous regression. Column (3) shows the results for ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` 2 2 ϕ1 ∆ShrWealthit ˆ CDFpσAgg qit ` ϕ2 ∆ShrWealthit ˆ CDFpσIdio qit ` εT,it ; it regresses total compensation on the same exogenous variables as the previous regressions. The standard errors are clustered by coperol (executive-firm unit).

39

40 2.207˚˚˚ (314.55) yes 126341

-0.671˚˚˚ (-12.46) yes 100767

(2) Equity 0.0137˚˚˚ (31.20) -0.00688˚˚˚ (-9.45) -0.00639˚˚˚ (-8.64) 0.000466˚˚˚ (3.55)

-0.664˚˚˚ (-12.30) yes 100589

(3) Total 0.0137˚˚˚ (31.14) -0.00689˚˚˚ (-9.45) -0.00639˚˚˚ (-8.65) 0.000463˚˚˚ (3.54)

1.603˚˚˚ (25.56) yes 126341

(4) Cash -0.000259˚˚˚ (-4.16) 0.000245˚˚ (2.39) -0.0000147 (-0.12) 0.0000345 (1.46) 1.258˚˚˚ (9.60)

-6.117˚˚˚ (-17.78) yes 100767

(5) Equity 0.0121˚˚˚ (26.92) -0.00644˚˚˚ (-9.01) -0.00517˚˚˚ (-7.00) 0.000448˚˚˚ (3.43) 11.39˚˚˚ (15.90)

-6.066˚˚˚ (-17.64) yes 100589

(6) Total 0.0121˚˚˚ (26.83) -0.00644˚˚˚ (-9.01) -0.00518˚˚˚ (-7.02) 0.000445˚˚˚ (3.42) 11.30˚˚˚ (15.77)

(7) Cash -0.0000385 (-0.61) -0.000154 (-1.45) 0.000157 (1.30) 0.0000322 (1.37) 1.240˚˚˚ (9.74) 3.565˚˚˚ (23.13) -0.394˚˚˚ (-2.70) -0.0242 (-0.25) yes 126341

(8) Equity 0.0116˚˚˚ (25.85) -0.00606˚˚˚ (-8.36) -0.00505˚˚˚ (-6.72) 0.000439˚˚˚ (3.35) 11.68˚˚˚ (16.17) -2.286˚˚˚ (-3.64) -3.790˚˚˚ (-5.89) -3.116˚˚˚ (-7.67) yes 100767

(9) Total 0.0116˚˚˚ (25.75) -0.00606˚˚˚ (-8.35) -0.00506˚˚˚ (-6.74) 0.000436˚˚˚ (3.34) 11.59˚˚˚ (16.04) -2.290˚˚˚ (-3.65) -3.747˚˚˚ (-5.83) -3.085˚˚˚ (-7.61) yes 100589

This table presents data results for different specifications of 3 different regression. Column (1) shows the results of: Cashit “ α0 ` 2 2 η ∆ShrWealthit ` α1 ∆ShrWealthit ˆ CDFpσAgg qit ` α2 ∆ShrWealthit ˆ CDFpσIdio qit ` γ1 ∆ShrWealthit ˆ T obinQCDF ` γ2 T obinQCDF ` it it 2 2 γ3 CDFpσAgg qit ` γ4 CDFpσIdio qit ` εC,it ; it regresses cash compensation on the change in shareholders’ wealth, the interaction between shareholders’ wealth and firm’s aggregate variance, the interaction between shareholders’ wealth and idiosyncratic variance, the interaction between shareholders’ wealth and Tobin’s Q, Tobin’s Q, firm’s aggregate variance, and idiosyncratic variance. Firm’s aggregate variance is calculated using the Fama and 2 French 3 factor model. Column (2) shows the results for ∆Equityit “ β0 ` ν ∆ShrWealthit ` β1 ∆ShrWealthit ˆ CDFpσAgg qit ` β2 ∆ShrWealthit ˆ 2 CDF CDF 2 2 CDFpσIdio qit ` ρ1 ∆ShrWealthit ˆ T obinQit ` ρ2 T obinQit ` ρ3 CDFpσAgg qit ` ρ4 CDFpσIdio qit ` εE,it ; it regresses equity-based compensation on the same exogenous variables as the previous regression. Column (3) shows the results for ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` ϕ1 ∆ShrWealthit ˆ 2 2 2 2 CDFpσAgg qit `ϕ2 ∆ShrWealthit ˆCDFpσIdio qit `ι1 ∆ShrWealthit ˆT obinQCDF `ι2 T obinQCDF `ι3 CDF pσAgg qit `ι4 CDF pσIdio qit `εT,it ; it regresses it it total compensation on the same exogenous variables as the previous regressions. The standard errors are clustered by coperol (executive-firm unit).

Coperol FE N t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01

Constant

2 CDFpσIdio q

2 CDFpσAgg q

T obinQCDF

∆W ealth ˆ T obinQCDF

2 ∆W ealth ˆ CDFpσIdio q

2 q ∆W ealth ˆ CDFpσAgg

∆W ealth

(1) Cash -0.0000755 (-1.32) 0.000197˚ (1.90) -0.000153 (-1.31) 0.0000362 (1.53)

Table 2: Data regression: CEO compensation and risk premia

Table 3: Data regression: CEO compensation and risk premia

∆W ealth 2 ∆W ealth ˆ CDFpσAgg q 2 ∆W ealth ˆ CDFpσIdio q

∆W ealth ˆ T obinQCDF T obinQCDF 2 q CDFpσAgg 2 q CDFpσIdio

BenchpAggq Constant Coperol FE N

(1) (2) Cash Equity -0.0000130 0.0115˚˚˚ (-0.21) (25.53) -0.000174 -0.00598˚˚˚ (-1.64) (-8.26) 0.000156 -0.00503˚˚˚ (1.29) (-6.67) 0.0000298 0.000447˚˚˚ (1.26) (3.40) ˚˚˚ 1.114 12.25˚˚˚ (8.75) (16.57) ˚˚˚ 3.535 -2.151˚˚˚ (22.97) (-3.41) ˚˚˚ -0.425 -3.654˚˚˚ (-2.91) (-5.67) 0.00648˚˚˚ -0.0290˚˚˚ (3.54) (-4.54) 0.0341 -3.376˚˚˚ (0.35) (-8.19) yes yes 126341 100767

(3) Total 0.0115˚˚˚ (25.43) -0.00597˚˚˚ (-8.25) -0.00504˚˚˚ (-6.70) 0.000445˚˚˚ (3.40) 12.16˚˚˚ (16.44) -2.157˚˚˚ (-3.43) -3.613˚˚˚ (-5.61) -0.0288˚˚˚ (-4.52) -3.344˚˚˚ (-8.12) yes 100589

t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01 This table presents data results for different specifications of 3 different regression. Column (1) shows the re2 2 qit `α2 ∆ShrWealthit ˆCDFpσIdio qit ` sults of: Cashit “ α0 `η ∆ShrWealthit `α1 ∆ShrWealthit ˆCDFpσAgg CDF 2 2 γ1 ∆ShrWealthit ˆ T obinQCDF ` γ T obinQ ` γ CDFpσ q ` γ CDFpσ q ` γ Bench ` ε 2 3 4 5 it C,it ; it it Agg it Idio it it regresses cash compensation on the change in shareholders’ wealth, the interaction between shareholders’ wealth and firm’s aggregate variance, the interaction between shareholders’ wealth and idiosyncratic variance, the interaction between shareholders’ wealth and Tobin’s Q, Tobin’s Q, firm’s aggregate variance, idiosyncratic variance, and the expected return in dollars. Firm’s aggregate variance is calculated using the Fama and French 3 factor model. Column (2) shows the results for ∆Equityit “ 2 2 β0 `ν ∆ShrWealthit `β1 ∆ShrWealthit ˆCDFpσAgg qit `β2 ∆ShrWealthit ˆCDFpσIdio qit `ρ1 ∆ShrWealthit ˆ CDF CDF 2 2 T obinQit ` ρ2 T obinQit ` ρ3 CDFpσAgg qit ` ρ4 CDFpσIdio qit ` ρ5 Benchit ` εE,it ; it regresses equity portfolio compensation on the same exogenous variables as the previous regression. Column (3) shows the results 2 2 for ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` ϕ1 ∆ShrWealthit ˆ CDFpσAgg qit ` ϕ2 ∆ShrWealthit ˆ CDFpσIdio qit ` CDF CDF 2 2 ι1 ∆ShrWealthit ˆ T obinQit ` ι2 T obinQit ` ι3 CDFpσAgg qit ` ι4 CDFpσIdio qit ` ι5 Benchit ` εT,it ; it regresses total compensation on the same exogenous variables as the previous regressions. The standard errors are clustered by coperol (executive-firm unit).

41

Table 4: Data regression: CEO compensation and risk premia (1) Cash ∆W ealth -0.000103˚ (-1.90) 2 ∆W ealth ˆ CDFpσRM q 0.000104 (1.56) 2 ∆W ealth ˆ CDFpσBM q -0.0000351 (-1.30) 2 q 0.0000469˚ ∆W ealth ˆ CDFpσSize (1.77) 2 ∆W ealth ˆ CDFpσIdio q -0.00000946 (-0.10) Constant 2.216˚˚˚ (375.48) Coperol FE yes N 126407

(2) Equity 0.0133˚˚˚ (30.77) -0.00163˚˚˚ (-4.02) 0.000494˚˚˚ (3.22) -0.0000458 (-0.39) -0.0113˚˚˚ (-19.37) -0.554˚˚˚ (-11.65) yes 100806

(3) Total 0.0133˚˚˚ (30.73) -0.00163˚˚˚ (-4.02) 0.000491˚˚˚ (3.21) -0.0000459 (-0.39) -0.0113˚˚˚ (-19.39) -0.546˚˚˚ (-11.45) yes 100628

t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01 This table presents data results for different specifications of 3 different regression. Column (1) shows the ř3 results of: Cashit “ α0 ` η ∆ShrWealthit ` j“1 αj ∆ShrWealthit ˆ CDFpσf2j qit ` α4 ∆ShrWealthit ˆ 2 CDFpσIdio qit ` εC,it ; it regresses cash compensation on the change in shareholders’ wealth, the interaction between shareholders’ wealth and the contribution to aggregate variance of each of the factors, and the interaction between shareholders’ wealth and idiosyncratic variance. The factor model used is the Fama and French 3 factor model. Column (2) shows the results for ∆Equityit “ β0 ` ν ∆ShrWealthit ` ř3 2 2 j“1 βj ∆ShrWealthit ˆ CDFpσfj qit ` β4 ∆ShrWealthit ˆ CDFpσIdio qit ` εE,it ; it regresses equity-based compensation on the same exogenous variables as the previous regression. Column (3) shows the results for ř3 2 ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` j“1 ϕj ∆ShrWealthit ˆ CDFpσf2j qit ` ϕ4 ∆ShrWealthit ˆ CDFpσIdio qit ` εT,it ; it regresses total compensation on the same exogenous variables as the previous regressions. The standard errors are clustered by coperol (executive-firm unit).

42

43 2.206˚˚˚ (301.20) yes 126341

-0.621˚˚˚ (-12.03) yes 100767

(2) Equity 0.0134˚˚˚ (31.15) -0.00144˚˚˚ (-3.52) 0.000355˚˚ (2.35) -0.0000597 (-0.47) -0.0117˚˚˚ (-19.62) 0.000388˚˚˚ (2.78)

` γ1 ∆ShrWealthit ˆ T obinQCDF it

` γ2 T obinQCDF it

-6.296˚˚˚ (-18.15) yes 100767

(5) Equity 0.0117˚˚˚ (26.72) -0.00136˚˚˚ (-3.41) 0.000304˚˚ (2.06) -0.0000656 (-0.52) -0.0101˚˚˚ (-16.71) 0.000377˚˚˚ (2.73) 11.86˚˚˚ (16.51)

-6.248˚˚˚ (-18.03) yes 100589

(6) Total 0.0117˚˚˚ (26.65) -0.00136˚˚˚ (-3.42) 0.000304˚˚ (2.06) -0.0000652 (-0.52) -0.0101˚˚˚ (-16.73) 0.000375˚˚˚ (2.72) 11.78˚˚˚ (16.40) 0.000120 (1.01) 0.0000306 (1.30) 1.296˚˚˚ (10.07) -0.0000325 (-0.31) 2.792˚˚˚ (21.19) -0.552˚˚˚ (-6.83) -0.261˚˚˚ (-3.28) 0.562˚˚˚ (6.37) yes 126341

(7) Cash -0.000118˚ (-1.90)

-0.00530˚˚˚ (-7.14) 0.000449˚˚˚ (3.43) 11.43˚˚˚ (15.97) -0.00615˚˚˚ (-8.51) -2.041˚˚˚ (-3.87) 0.659˚ (1.81) -1.135˚˚˚ (-3.08) -4.827˚˚˚ (-11.72) yes 100767

(8) Equity 0.0120˚˚˚ (26.56)

-0.00531˚˚˚ (-7.16) 0.000446˚˚˚ (3.42) 11.34˚˚˚ (15.85) -0.00615˚˚˚ (-8.50) -2.015˚˚˚ (-3.83) 0.634˚ (1.75) -1.126˚˚˚ (-3.06) -4.783˚˚˚ (-11.62) yes 100589

(9) Total 0.0120˚˚˚ (26.47)

j

The standard errors are clustered by coperol (executive-firm unit).

j

between shareholders’ wealth and Tobin’s Q, Tobin’s Q, the contribution to aggregate variance of each of the factors, and idiosyncratic variance. The factor model used is the Fama and French 3 factor model. ř 2 2 CDF Column (2) shows the results for ∆Equityit “ β0 ` ν ∆ShrWealthit ` 3 ` ρ2 T obinQCDF ` j“1 βj ∆ShrWealthit ˆ CDFpσfj qit ` β4 ∆ShrWealthit ˆ CDFpσIdio qit ` ρ1 ∆ShrWealthit ˆ T obinQit it ř3 2 2 j“1 ρj`2 CDFpσfj qit ` ρ6 CDFpσIdio qit ` εE,it ; it regresses equity-based compensation on the same exogenous variables as the previous regression. Column (3) shows the results for ∆Totalit “ ř ř 2 2 CDF 2 2 ϕ0 ` δ ∆ShrWealthit ` 3 ` ι2 T obinQCDF ` 3 j“1 ϕj ∆ShrWealthit ˆ CDFpσfj qit ` ϕ4 ∆ShrWealthit ˆ CDFpσIdio qit ` ι1 ∆ShrWealthit ˆ T obinQit it j“1 ιj`2 CDFpσfj qit ` ι6 CDFpσIdio qit ` εT ,it ; ř3 2 2 it regresses total compensation on the same exogenous variables as the previous regressions. For columns (7)-(9) I use ϕ1 ∆ShrWealthit ˆ CDFpσAgg qit instead of j“1 ϕj ∆ShrWealthit ˆ CDFpσf qit .

wealth, the interaction between shareholders’ wealth and the contribution to aggregate variance of each of the factors, the interaction between shareholders’ wealth and idiosyncratic variance, the interaction

2 α4 ∆ShrWealthit ˆ CDFpσIdio qit

1.603˚˚˚ (25.62) yes 126341

(4) Cash -0.000274˚˚˚ (-4.58) 0.000141˚˚ (2.13) -0.0000556˚˚ (-2.05) 0.0000457˚ (1.72) 0.000110 (1.16) 0.0000503˚˚ (2.26) 1.256˚˚˚ (9.59)

ř 2 Column (1) shows the results of: Cashit “ α0 ` η ∆ShrWealthit ` 3 j“1 αj ∆ShrWealthit ˆ CDFpσfj qit ` ř3 2 2 ` j“1 γj`2 CDFpσf qit ` γ6 CDFpσIdio qit ` εC,it ; it regresses cash compensation on the change in shareholders’

-0.612˚˚˚ (-11.83) yes 100589

(3) Total 0.0134˚˚˚ (31.10) -0.00144˚˚˚ (-3.53) 0.000353˚˚ (2.34) -0.0000598 (-0.47) -0.0117˚˚˚ (-19.64) 0.000386˚˚˚ (2.77)

This table presents data results for different specifications of 3 different regression.

Coperol FE N t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01

Constant

2 CDFpσSize q

2 CDFpσBM q

2 q CDFpσRM

2 ∆W ealth ˆ CDFpσAgg q

T obinQCDF

∆W ealth ˆ T obinQCDF

2 ∆W ealth ˆ CDFpσIdio q

2 ∆W ealth ˆ CDFpσSize q

2 q ∆W ealth ˆ CDFpσBM

2 q ∆W ealth ˆ CDFpσRM

∆W ealth

(1) Cash -0.0000916˚ (-1.67) 0.000133˚˚ (2.00) -0.0000504˚ (-1.86) 0.0000465˚ (1.76) -0.0000724 (-0.78) 0.0000512˚˚ (2.30)

Table 5: Data regression: CEO compensation and risk premia

Table 6: Data regression: CEO turnover and risk premia (1) turnover -13.76˚˚˚ (-2.70)

(2) turnover -13.15˚˚ (-2.57)

σIdio

31.95˚˚˚ (10.43)

31.42˚˚˚ (10.20)

RetpAggq

-0.289˚ (-1.66)

-0.286 (-1.63)

RetpIdioq

-0.612˚˚˚ (-6.32)

-0.611˚˚˚ (-6.32)

σAgg

-1.822˚˚˚ (-3.62)

Equity ´ basedpay ą 0 -3.897˚˚˚ (-42.97) yes 20821

Constant Firm FE N

-2.078˚˚˚ (-4.08) yes 20821

t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01 This table presents data results for different specifications of: P rpForcedit q “ F pα ` γσAggit ` ρσIdioit ` ς 1 Xit ` it ), where Forcedit is a dummy variable that is equal to one if the CEO was fired in year t and zero otherwise (based on a news analysis), σAggit is a variable that measures firm’s aggregate risk, σIdioit is a variable that measures idiosyncratic risk, and Xit is a set of controls. For column (1) the controls are: The stock’s expected return, the mean idiosyncratic return in the past year. Column (2) includes as control the variable Equity-based payą0, it is a dummy variable that is equal to one if equity-based pay is greater than zero and zero otherwise. The Fama and French 3 factor model is used to obtain systematic and idiosyncratic measures. The standard errors are clustered at the firm level.

44

Table 7: Monthly calibration Parameter

Description

Model

Subjective discount factor Elasticity of intertemporal substitution Risk aversion

0.99 2.0 5.0

δ σ

Subjective discount factor Risk aversion

0.95 1.2



Effort curvature

2.0

ζ

Scaling parameter of the marginal cost of effort

2.5

C. Consumption g¯ ρg σg

Average consumption growth rate Persistence of consumption growth Conditional volatility of consumption growth

A. Preferences Shareholder β ψ γ B. Preferences CEO

0.019/12 0.92 0.0015

This table reports the monthly calibration. Panel A reports the preferences parameters for the representative shareholder. Panel B presents the preference parameters for the managers. Finally, panel C reports the parameters of aggregate consumption process

Table 8: Contract and returns moments Statistic

Data

Model

ErCashs{Er∆Equitys

1.1

0.9

σrCashs{σr∆Equitys

0.23

0.2

corrpCash, ∆Equityq Value Premium (basis points monthly)

-0.12 40

-0.25 30

This table reports the moments matched by the model and their data counterpart.

45

Table 9: Comparison data and model: compensation Cash Data Model (1) (2) -0.0000886 0.0103993 (-1.53)

∆W ealth

Equity Data Model (3) (4) 0.0135 0.017356 (30.64)

2 ∆W ealth ˆ CDFpσAgg q

0.000168 (1.64)

0.0067455

-0.00720 (-9.76)

-0.011941

2 ∆W ealth ˆ CDFpσIdio q

-0.0000839 (-0.75)

-0.0165998

-0.00546 (-7.41)

-0.0069235

This table presents data results for different specifications of 2 different regression. Column (1) and (2) show the results of: Cashit “ α0 ` η ∆ShrWealthit ` α1 ∆ShrWealthit ˆ 2 2 CDFpσAgg qit ` α2 ∆ShrWealthit ˆ CDFpσIdio qit ` εC,it ; it regresses cash compensation for the data and the model on the change in shareholders’ wealth, the interaction between shareholders’ wealth and firm’s aggregate variance, and the interaction between shareholders’ wealth and idiosyncratic variance. Firm’s aggregate variance is calculated using the Fama and French 3 factor model for the data. Column (3) and (4) show the results for ∆Equityit “ 2 2 qit `β2 ∆ShrWealthit ˆCDFpσIdio qit `εE,it ; β0 `ν ∆ShrWealthit `β1 ∆ShrWealthit ˆCDFpσAgg it regresses equity-based compensation for the data and the model on the same exogenous variables as the previous regression.

Table 10: Comparison data and model: turnover

σAgg σIdio RetpAggq RetpIdioq

Turnover Data Model (1) (2) -13.1536 -74.823 (-2.57) 31.4177 2.17342 (10.20) -0.286363 0.02242 (-1.63) -0.6134 2.86964 (-6.32)

This table presents data results for the data and the model of: P rpForcedit q “ F pα ` γσAggit ` ρσIdioit ` it ), where Forcedit is a dummy variable that is equal to one if the CEO was fired in year t and zero otherwise (based on a news analysis), σAggit is the firm’s aggregate risk, and σIdioit is the idiosyncratic risk. The Fama and French 3 factor model is used to obtain firm’s aggregate and idiosyncratic measures for the data. The standard errors are clustered at the firm level.

46

Table 11: Comparative statics: compensation Model A. Cash compensation 2 ∆W ealth ˆ CDFpσAgg qit 2 ∆W ealth ˆ CDFpσIdio qit B. Equity compensation 2 ∆W ealth ˆ CDFpσAgg qit 2 ∆W ealth ˆ CDFpσIdio qit C. Turnover σAgg σIdio

Data (1) 0.000168 -0.0000839

Benchmark (2) 0.0067455 -0.0165998

δ “ 0.9 (3) 0.015257 -0.0284832

CRRA (4) 0.0067815 -0.0164617

Risk Neutral (5) -0.0023201 -0.0023489

σ“2 (6) 0.0496758 -0.1520065

ζ “ 0.5 (7) -0.0008742 0.0076301

-0.0072 -0.00546

-0.011941 -0.0069235

-0.0032341 -0.0398544

-0.0023296 -0.0265555

0.0014339 -0.0193543

-0.000335 -0.0464216

0.0059709 -0.0479778

-13.1536 31.4177

-74.8223 2.1734

-63.81425 1.57597

-67.3666 2.15754

43.34675 4.438744

7.0762 -0.49074

-85.3593 2.2637

This table compares alternative calibrations of the benchmark model for cash compensation, equity-based compensation and turnover. Model benchmark is the benchmark model. Model δ “ 0.9 lowers the subjective discount rate of the CEO from the benchmark value of 0.95 to 0.9. Model CRRA lowers the elasticity of intertemporal substitution from the benchmark value of 2 to 1/5 (the reciprocal of the risk aversion) for the representative shareholder. In column 5 the representative shareholder is risk neutral. Model σ “ 2 increases the risk aversion parameters of the managers from 1 to 2. Model ζ “ 0.5 decreases the marginal cost of effort from 2.5 to 0.5.

47

Table 12: Data regression: CEO compensation and risk premia (1) Cash ∆W ealth -0.0000967˚ (-1.67) 2 ∆W ealth ˆ CDFpσAgg q 0.000160 (1.50) 2 ∆W ealth ˆ CDFpσIdio q -0.0000675 (-0.58) Constant 2.215˚˚˚ (402.37) Coperol FE yes N 126407

(2) Equity 0.0135˚˚˚ (30.58) -0.00809˚˚˚ (-10.53) -0.00458˚˚˚ (-6.01) -0.584˚˚˚ (-11.96) yes 100806

(3) Total 0.0135˚˚˚ (30.53) -0.00809˚˚˚ (-10.53) -0.00458˚˚˚ (-6.03) -0.579˚˚˚ (-11.78) yes 100628

t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01 This table presents data results for different specifications of 3 different regression. Column (1) shows 2 the results of: Cashit “ α0 ` η ∆ShrWealthit ` α1 ∆ShrWealthit ˆ CDFpσAgg qit ` α2 ∆ShrWealthit ˆ 2 CDFpσIdio qit ` εC,it ; it regresses cash compensation on the change in shareholders’ wealth, the interaction between shareholders’ wealth and firm’s aggregate variance, and the interaction between shareholders’ wealth and idiosyncratic variance. Firm’s aggregate variance is calculated using the 4 factor model. Column (2) 2 qit `β2 ∆ShrWealthit ˆ shows the results for ∆Equityit “ β0 `ν ∆ShrWealthit `β1 ∆ShrWealthit ˆCDFpσAgg 2 CDFpσIdio qit ` εE,it ; it regresses equity portfolio compensation on the same exogenous variables as the previous regression. Column (3) shows the results for ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` ϕ1 ∆ShrWealthit ˆ 2 2 CDFpσAgg qit `ϕ2 ∆ShrWealthit ˆCDFpσIdio qit `εT,it ; it regresses total compensation on the same exogenous variables as the previous regressions. The standard errors are clustered by coperol (executive-firm unit).

48

49 2.208˚˚˚ (316.65) yes 126341

-0.673˚˚˚ (-12.47) yes 100767

(2) Equity 0.0137˚˚˚ (31.19) -0.00769˚˚˚ (-10.17) -0.00558˚˚˚ (-7.34) 0.000455˚˚˚ (3.44)

-0.667˚˚˚ (-12.32) yes 100589

(3) Total 0.0138˚˚˚ (31.13) -0.00769˚˚˚ (-10.18) -0.00558˚˚˚ (-7.35) 0.000453˚˚˚ (3.43)

1.600˚˚˚ (25.50) yes 126341

(4) Cash -0.000268˚˚˚ (-4.31) 0.000251˚˚ (2.35) -0.0000113 (-0.09) 0.0000344 (1.45) 1.265˚˚˚ (9.65)

-6.104˚˚˚ (-17.74) yes 100767

(5) Equity 0.0121˚˚˚ (26.90) -0.00722˚˚˚ (-9.73) -0.00440˚˚˚ (-5.79) 0.000435˚˚˚ (3.31) 11.36˚˚˚ (15.85)

-6.053˚˚˚ (-17.61) yes 100589

(6) Total 0.0121˚˚˚ (26.82) -0.00722˚˚˚ (-9.73) -0.00441˚˚˚ (-5.81) 0.000432˚˚˚ (3.30) 11.27˚˚˚ (15.73)

(7) Cash -0.0000466 (-0.74) -0.000168 (-1.52) 0.000181 (1.46) 0.0000308 (1.31) 1.268˚˚˚ (9.96) 3.671˚˚˚ (23.54) -0.523˚˚˚ (-3.59) -0.0260 (-0.26) yes 126341

(8) Equity 0.0116˚˚˚ (25.84) -0.00686˚˚˚ (-9.14) -0.00424˚˚˚ (-5.50) 0.000425˚˚˚ (3.22) 11.68˚˚˚ (16.14) -1.736˚˚˚ (-2.74) -4.227˚˚˚ (-6.51) -3.183˚˚˚ (-7.82) yes 100767

(9) Total 0.0116˚˚˚ (25.75) -0.00686˚˚˚ (-9.12) -0.00426˚˚˚ (-5.53) 0.000423˚˚˚ (3.21) 11.59˚˚˚ (16.01) -1.738˚˚˚ (-2.74) -4.184˚˚˚ (-6.45) -3.152˚˚˚ (-7.76) yes 100589

This table presents data results for different specifications of 3 different regression. Column (1) shows the results of: Cashit “ α0 ` 2 2 η ∆ShrWealthit ` α1 ∆ShrWealthit ˆ CDFpσAgg qit ` α2 ∆ShrWealthit ˆ CDFpσIdio qit ` γ1 ∆ShrWealthit ˆ T obinQCDF ` γ2 T obinQCDF ` it it 2 2 γ3 CDFpσAgg qit ` γ4 CDFpσIdio qit ` εC,it ; it regresses cash compensation on the change in shareholders’ wealth, the interaction between shareholders’ wealth and firm’s aggregate variance, the interaction between shareholders’ wealth and idiosyncratic variance, the interaction between shareholders’ wealth and Tobin’s Q, Tobin’s Q, firm’s aggregate variance, and idiosyncratic variance. Firm’s aggregate variance is calculated using the 4 factor 2 2 model. Column (2) shows the results for ∆Equityit “ β0 ` ν ∆ShrWealthit ` β1 ∆ShrWealthit ˆ CDFpσAgg qit ` β2 ∆ShrWealthit ˆ CDFpσIdio qit ` CDF CDF 2 2 ρ1 ∆ShrWealthit ˆ T obinQit ` ρ2 T obinQit ` ρ3 CDFpσAgg qit ` ρ4 CDFpσIdio qit ` εE,it ; it regresses equity portfolio compensation on the same 2 exogenous variables as the previous regression. Column (3) shows the results for ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` ϕ1 ∆ShrWealthit ˆ CDFpσAgg qit ` 2 CDF CDF 2 2 ϕ2 ∆ShrWealthit ˆ CDFpσIdio qit ` ι1 ∆ShrWealthit ˆ T obinQit ` ι2 T obinQit ` ι3 CDF pσAgg qit ` ι4 CDF pσIdio qit ` εT,it ; it regresses total compensation on the same exogenous variables as the previous regressions. The standard errors are clustered by coperol (executive-firm unit).

Coperol FE N t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01

Constant

2 CDFpσIdio q

2 q CDFpσAgg

T obinQCDF

∆W ealth ˆ T obinQCDF

2 ∆W ealth ˆ CDFpσIdio q

2 q ∆W ealth ˆ CDFpσAgg

∆W ealth

(1) Cash -0.0000826 (-1.45) 0.000197˚ (1.84) -0.000146 (-1.21) 0.0000364 (1.53)

Table 13: Data regression: CEO compensation and risk premia

Table 14: Data regression: CEO compensation and risk premia

∆W ealth 2 ∆W ealth ˆ CDFpσAgg q 2 ∆W ealth ˆ CDFpσIdio q

∆W ealth ˆ T obinQCDF T obinQCDF 2 q CDFpσAgg 2 q CDFpσIdio

BenchpAggq Constant Coperol FE N

(1) (2) Cash Equity -0.0000214 0.0115˚˚˚ (-0.34) (25.53) ˚ -0.000194 -0.00677˚˚˚ (-1.75) (-9.05) 0.000185 -0.00424˚˚˚ (1.49) (-5.50) 0.0000282 0.000434˚˚˚ (1.19) (3.28) ˚˚˚ 1.142 12.24˚˚˚ (8.96) (16.54) ˚˚˚ 3.647 -1.631˚˚ (23.43) (-2.56) ˚˚˚ -0.561 -4.064˚˚˚ (-3.85) (-6.26) 0.00656˚˚˚ -0.0290˚˚˚ (3.58) (-4.54) 0.0325 -3.440˚˚˚ (0.33) (-8.33) yes yes 126341 100767

(3) Total 0.0115˚˚˚ (25.43) -0.00676˚˚˚ (-9.03) -0.00425˚˚˚ (-5.52) 0.000432˚˚˚ (3.27) 12.16˚˚˚ (16.41) -1.634˚˚ (-2.57) -4.023˚˚˚ (-6.20) -0.0288˚˚˚ (-4.53) -3.408˚˚˚ (-8.27) yes 100589

t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01 This table presents data results for different specifications of 3 different regression. Column (1) shows the re2 2 qit `α2 ∆ShrWealthit ˆCDFpσIdio qit ` sults of: Cashit “ α0 `η ∆ShrWealthit `α1 ∆ShrWealthit ˆCDFpσAgg CDF 2 2 γ1 ∆ShrWealthit ˆ T obinQCDF ` γ T obinQ ` γ CDFpσ q ` γ CDFpσ q ` γ Bench ` ε 2 3 4 5 it C,it ; it it Agg it Idio it it regresses cash compensation on the change in shareholders’ wealth, the interaction between shareholders’ wealth and firm’s aggregate variance, the interaction between shareholders’ wealth and idiosyncratic variance, the interaction between shareholders’ wealth and Tobin’s Q, Tobin’s Q, firm’s aggregate variance, idiosyncratic variance, and the expected return in dollars. Firm’s aggregate variance is calculated using the 4 factor model. Column (2) shows the results for ∆Equityit “ β0 ` ν ∆ShrWealthit ` 2 2 β1 ∆ShrWealthit ˆ CDFpσAgg qit ` β2 ∆ShrWealthit ˆ CDFpσIdio qit ` ρ1 ∆ShrWealthit ˆ T obinQCDF ` it CDF 2 2 ρ2 T obinQit ` ρ3 CDFpσAgg qit ` ρ4 CDFpσIdio qit ` ρ5 Benchit ` εE,it ; it regresses equity portfolio compensation on the same exogenous variables as the previous regression. Column (3) shows the results for 2 2 ∆Totalit “ ϕ0 ` δ ∆ShrWealthit ` ϕ1 ∆ShrWealthit ˆ CDFpσAgg qit ` ϕ2 ∆ShrWealthit ˆ CDFpσIdio qit ` CDF CDF 2 2 ι1 ∆ShrWealthit ˆ T obinQit ` ι2 T obinQit ` ι3 CDFpσAgg qit ` ι4 CDFpσIdio qit ` ι5 Benchit ` εT,it ; it regresses total compensation on the same exogenous variables as the previous regressions. The standard errors are clustered by coperol (executive-firm unit).

50

Table 15: Data regression: CEO turnover and risk premia table (1) turnover -13.75˚˚˚ (-2.71)

(2) turnover -13.15˚˚ (-2.57)

σIdio

32.33˚˚˚ (10.40)

31.79˚˚˚ (10.17)

RetpAggq

-0.358˚˚ (-2.10)

-0.355˚˚ (-2.08)

RetpIdioq

-0.620˚˚˚ (-6.34)

-0.619˚˚˚ (-6.33)

σAgg

-1.825˚˚˚ (-3.62)

Equity ´ basedpay ą 0 -3.884˚˚˚ (-43.35) yes 20821

Constant Firm FE N

-2.062˚˚˚ (-4.03) yes 20821

t statistics in parentheses ˚ p ă 0.10, ˚˚ p ă 0.05, ˚˚˚ p ă 0.01 This table presents data results for different specifications of: P rpForcedit q “ F pα ` γσAggit ` ρσIdioit ` ς 1 Xit ` it q, where Forcedit is a dummy variable that is equal to one if the CEO was fired in year t and zero otherwise (based on a news analysis), σAggit is a variable that measures firm’s aggregate risk, σIdioit is a variable that measures idiosyncratic risk, and Xit is a set of controls. For column (1) the controls are: The stock’s expected return, the mean idiosyncratic return in the past year. Column (2) includes as control the variable Equity-based payą0, it is a dummy variable that is equal to one if equity-based pay is greater than zero and zero otherwise. The 4 factor model is used to obtain aggregate and idiosyncratic measures. The standard errors are clustered at the firm level.

51