Executive Compensation-Implied CEO Risk-Taking and Systemic Risk of Bank Holding Companies

Transcription

1 Executive Compensation-Implied CEO Risk-Taking and Systemic Risk of Bank Holding Companies G. Nathan Dong 1 Columbia University May 27th, 2018 ABSTRACT When a manager accepts the offer of employment to become the CEO of the firm, his compensation contract that is supposedly intended to maximize the value of the firm and his personal utility reveals the risk preference of this new CEO. Assuming the observed executive compensation implements best effort and the compensation contract is optimal; the principalagent model is fitted to show a relatively high level of risk-taking among CEOs in the United States. Both the non-firm wealth of the CEOs and the moneyness of their option holdings are negatively related to their implied risk-aversion. Across industries, CEOs in wholesale trade are, on the average, the most risk-averse, whereas financial institutions rank fourth behind those in retail trade, construction, and agriculture industries in terms of risk-taking. More importantly, the relation between the degree of risk-taking of a bank CEO and the amount of systemic risk that the bank contributes to the entire financial system is very weak. Keywords: CEO compensation, risk taking, systemic risk, bank holding companies JEL Classification: G20, G21, D86, J33 1 Assistant Professor of Financial Management, Department of Health Policy and Management, Columbia University. 722 West 168th Street, New York, NY, USA. Tel: gd2243@columbia.edu. We thank Craig Brown, Ruediger Fahlenbrach, Steve Kou, and participants in the National University of Singapore (NUS) Annual Risk Management Conference, Portsmouth-Fordham Conference on Banking and Finance, The Second Shanghai Risk Forum (SHUFE). All errors remain our responsibility.

2 In recent years, anti-regulatory ideology kept the United States from modernizing the rules of the capitalist game in a period of intense financial innovation and perverse incentives to creep in. Alice Rivlin s Testimony before the House Committee on Financial Service, July 21, Shareholders interest in more risk-taking implies that they could benefit from providing executives with excessive incentives in this direction. Executives with such incentives can use their informational advantages, and whatever discretion they have been left by existing regulations, to increase risks. Financial Times, August 3, I. Introduction Despite a large body of studies on estimating the distribution of individuals risk preferences in various settings, prior literature of inferring the degree of risk aversion (or concavity of marginal utility) of decision makers such as corporate executives is scarce, and little research has been done to examine the link between an executive s risk preference and the characteristics of both the manager and the company. Senior executives play a critical role in not only formulating business strategy and ensuring operational efficiency but also answering for financial performance to the shareholders. Understanding the heterogeneity of their risk preferences is important in order to link risk-taking incentives embedded in executive compensation contracts to managerial and strategic decisions, such as altering capital structure, hoarding cash, allocating capital investments, manipulating accounting numbers, and committing financial fraud. Therefore, the question of whether senior executives of publicly traded companies exhibit high or low degree of risk aversion becomes a relevant concern and has not been conclusively resolved. More importantly, in the banking sector, financial innovations such as securitization with which bank assets (mainly mortgages) can be easily sold to other investors offer financial services firms the advantage of reduced cost of asset sales that eventually causes higher levels of risky lending (Santomero and Trester 1998). The public anger over the executive compensation at financial firms coupled with common beliefs that compensation-induced excessive risk-taking was the root cause of the financial crisis (see the quotes above 4 ) led to the question of whether top executives of financial services firms 2 Excerpt from Rivlin (2009). 3 Except from Bebchuk (2009). 4 For the detailed discussion of this issue in EU countries, see Murphy (2013). 2

3 actually responded to compensation incentives to take excessive risks that eventually led to the crisis. The main challenge to answer this question lies in the fact that it is difficult, if not possible, to quantify or measure risk preferences of corporate executives in a laboratory setting. Even a controlled experiment is conducted it is very likely that their risky choice in the lab situation does not resemble the decision-making behavior they might display in the real-world business environment. In this paper, we propose a calibration method to recover risk-aversion measures of corporate executives from their observed compensation contracts. It is well known that individuals with different degrees of risk aversion choose different types of contracts (Ackerberg and Botticini 2002; Allen and Lueck 1995). In the context of executive compensation design, the decision that a manager serves as CEO of the firm and receives compensation in the form of stock and options is materially affected by the interaction of risk preference and compensation structure (e.g., cash salary, stock and options). On the one hand, CEOs with a certain level of risk-aversion choose to work for firms offering compensation contracts with embedded risk profiles that match those of CEOs, and on the other hand, holding executive stock and options may increase or decrease managerial risk taking, as illustrated theoretically by Ross (2004) and empirically by Lewellen (2006), among others. In equilibrium, the compensation contract maximizes the firm value and the CEO s utility, and the observed contract implements the CEO s optimal action. Therefore, fitting the standard principal-agent model using observed executive compensation contracts can reveal the CEOs risk preferences. This research contributes to existing evidence on estimating the implied risk aversion and relating the degree of risk-taking of bank CEOs to the level of systemic risk (i.e., the amount of risk that each individual bank contributes to the entire financial system). There is a voluminous literature on option-implied risk preferences, surveyed by Bliss and Panigirtzoglou (2002). For example, risk preferences can be estimated by applying the semi-parametric method of Aït-Sahalia and Lo (1998, 2000) for estimation of the option-implied density function in two steps. The first step estimates implied strike prices from the deltas as a smooth function, following Bliss and Panigirtzoglou (2004) and Kang and Kim (2006), and the second step plugs the GBS volatility function in a lognormal density. As a final step, the Aït-Sahalia and Lo estimator yields relative risk aversion and marginal rate of substitution, both depending on the stock price. However, this type of estimation method only produces firm-level risk preference, 3

4 and unfortunately, it offers little help in understanding the degree of risk-aversion on the CEO level. These issues are in focus after the introduction of accounting standards IFRS 2 (see International Accounting Standards Board, 2004), SAB 107, and FAS 123R (see Securities and Exchange Commission, 2005), and the Dodd-Frank Wall Street Reform and Consumer Protection Act (see Securities and Exchange Commission, 2015), requiring publicly traded firms to expense the value of executive stock options and to disclose the ratio of the CEO compensation to the median compensation of its employees. In contrast to common practice, this paper extends the principal-agent models of Holmstrom (1979), Dittmann and Maug (2007), and Armstrong, Larcker and Su (2007) and calibrate the model with observed cash salary, stock and options in executive compensation contracts to estimate the risk-aversion of individual CEOs. As the first paper to address the question if executive compensation contributed to the financial crisis, Fahlenbrach and Stulz (2011) find no evidence that banks with CEOs whose incentives were better aligned with the interests of their shareholders performed better during the crisis. Also evidence indicates that these banks actually performed worse. Banks whose CEOs had better incentives in terms of the dollar value of their stake in the company performed significantly worse than banks where CEOs had poorer incentives. This implies that incentive compensation had no adverse impact on bank performance during the crisis. While many of the bank CEOs made high cost, bad bets that cost themselves and their shareholders, the data suggests that CEOs took these bets because they believed they would be profitable for the shareholders. On the contrary, Bennett, Guntay and Unal (2012) show that banks with CEOs holding more inside-debt relative to equity in 2006, experienced higher default risk and lower stock returns in The closest paper to our risk-aversion estimation approach is Brenner (2015), who estimates the risk preferences of U.S. executives from data on the exercising of employee stock options. Its calibration method makes use of the assumption that these senior corporate managers (as option holders) choose the stock prices at which to exercise the options such as to maximize their subjective value. Such approach has the advantage of relying on a simplistic argument over the optimal choice of the share price that triggers the option exercise to identify the risk preferences, while our approach requires a condition of optional contract, meaning the executive would only be offered a contract of employment to serve as the CEO of the firm if the compensation reflected the optimal level of efforts that the CEO-elect would exert in order 4

5 to maximize the firm value. Nonetheless, our calibration result of the average Arrow-Pratt measure of relative risk-aversion being 4.6 for 290 long-serving CEOs in the United States, to some extent, is consistent with the finding in Brenner (2015) that senior executives are more risk taking than managers of lower rank. What is more interesting in our study is that the mean level of risk aversion of American CEOs remains stable (between 4.2 to 5.5) over a long period of time from 1997 to 2013, as shown in Figure 1, except a slight fluctuation between 2004 and However, the box plot of upper adjacent value, 75th percentile, median, 25th percentile, and lower adjacent values presents a slightly different picture: the distribution changes dramatically over time and since 2001, the median level of risk-aversion has been gradually declining, with some fluctuations, and reached the lowest level in 2005 and 2006 before bouncing back again in 2007 and To some extent, this evidence may support the argument that excessive risk-taking was a major contributing factor of the recent financial crisis of , at least on the aggregate; however, when we actually use two measures of systemic risk that proxy for the amount of risk that an individual bank contribute to the entire financial system (SES and CoVaR), 5 the relationship between bank CEO risk-aversion and systemic risk vanishes. [Insert Figure 1 Here] The remainder of the paper is organized as follows. Section II reviews the relevant prior research. Section III specifies the theoretical model and empirical method in detail. Section IV describes the sample data. Section V presents empirical results. Section VI discusses the implication and concludes. II. Related Literature This paper is related to four strands of literature. The first set of related studies provide some evidence on the risk preferences of executives, for example, Grahama, Harvey and Puri (2013) for privately held firms. In a more recent study, Cain and McKeon (2016) use the possession of a FAA (Federal Aviation Administration) pilot license and living near a major airport to identify risk-seekers among executives and find that risk-seeking pilot CEOs engage in more acquisitions that eventually lead to positive value creation. Corporate senior executives represent a demographic group that is often associated with a very special set of socioeconomic 5 SES (Acharya et al. 2016) in and CoVaR (Adrian and Brunnermeier 2016). 5

6 characteristics and psychological traits (e.g., Harvard dropout, Marine Corps veteran), all of which may correlate with risk preferences. On the one hand, they often invested in human and social capital during their early careers that allow them to be competitive and entrepreneurial, and the propensity to make such investments is related to risk aversion (Shaw 1996), and on the other hand, the selection of CEOs is generally on the basis of merit and competitive examination and Skaperdas and Gan (1995) argue that the probability of becoming a CEO after a comprehensive selection process may itself be a function of risk aversion. Therefore, it is often not feasible to extrapolate from studies of risk aversion from non-executives data (Borghans, Lex, James Heckman, Bart Golsteyn, and Huub Meijers 2009; Dohmen, Falk, Huffmann and Sunde 2010; MacCrimmon and Wehrung 1990). Second, starting with an influential paper by Jensen and Meckling (1976), a literature in finance attempts to explain to what extent equity-based compensation contracts induce managerial risk taking. Later on, Carpenter (2000) and Ross (2004) argue the inducing effect of options based compensation on risk taking depends on the manager s utility function, because increasing the wealth of the executive may move into more or less risk-averse portions of the utility function. Concentrating on volatility costs of debt, Lewellen (2006) finds that managers holding in-the-money options are typically worse off by an increase in leverage, based on certainty equivalent of wealth. Lambert, Larcker and Verrecchia (1991) suggests that the managerial incentives provided by compensation contracts do not necessarily follow from the application of market-based valuation formulas. Hall and Murphy (2002) estimates options values using certainty equivalence approach, similar to Lambert, Larcker and Verrecchia (1991), and claim that granting at-the-money options maximizes incentives when grants are an add-on to existing pay packages, while restricted stock is preferred when grants are accompanied by reductions in cash compensation. Meulbroek (2001) provides empirical evidences that managers value stock or option-based compensation at less than its market value, because undiversified managers are exposed to the firm s total risk but rewarded for the systematic risk. Kadan and Swinkels (2008) find that options can dominate stocks as a means of motivation only if default risk is not substantial, regardless of the exiting portfolio of the manager. Aseff and Santos (2005) explain why most stock options are granted at the money using the intermediate role of the strike price, and in turn suggest that a relatively small 6

7 additional cost to the principal in compensation such as the use of simple stock options can incentivize the agent to exert high effort. A third related literature use calibration technique of option pricing models, such as by eliciting subjective option values from calibrating utility models to observed exercise pattern by employees (e.g., Ingersoll 2006; Bettis, Bizjak and Lemmon 2005). A small subset of these studies ask if the observed compensation contract reflects the optimal level of the CEO s effort, we can actually find another contract, with a new mix of salary, stock and options, which will cost less to the firm. In a typical principal-agent model, to maximize financial returns, the principal has to incentivize the agent to exert the optimal level of effort and in turn take the appropriate amount of risk (Holmstrom and Milgrom 1987). However, the difficulty to find an optimal managerial compensation contract lies in the fact that we cannot quantify the optimal level of the CEO s effort. Dittmann and Maug (2007) assume the observed compensation contracts implement the optimal action, meaning the beginning stock price anticipates the optimal effort that will be selected by the agent for a given compensation contract. This assumption simplifies the classical principal-agent problem to a principal-only problem. Their model predicts that optimal compensation schemes should have no or at best miniscule holdings of stock options, and incentives should be provided through restricted stock. Finally, Armstrong, Larcker and Su (2007) avoid the use of first order approach as in Dittmann and Maug (2007) and reach the exact opposite conclusion that stock options are an important part of the optimal CEO compensation contact. Most of these papers do not calibrate a principal-agent model explicitly to back out the CEO s managerial risk aversion. This paper takes a step further and proposes a new numerical calibration approach to back out the degree of managerial risk preference by assuming not only the optimal effort but also the optimal contract, meaning that the observed executive compensation has already attained the level at the lowest cost to the firm. In previous studies, Hall and Murphy (2000) and Hall and Murphy (2002) use assumed risk aversion coefficients, because empirical estimates are few and exhibit significant variation. This paper contributes to the literature by estimating relative risk-aversion based on executive compensation data including cash-based salary, stock and options. Of course, this paper is also closely related to the literature on systemic risk. The contagion effect of an event usually refers to the spillover effects of stocks of one or more firms 7

8 to others (Kaufman 1994), but has also been characterized as the change in the value of a firm that can be attributed to economic events with a clearer and more direct impact on some other firm (Docking, Scott, Hirschey, and Jones 1997). Contagion has been studied widely in the theoretical and empirical financial literature (for reviews see Flannery 1998). The focus of analysis has ranged from strong systemic shocks involving multiple bank failures, currency crises, and market crashes to informational spillover effects that lead to the revaluation of stock prices but not to widespread failures. This paper contributes to this body of literature by connecting a bank CEO s risk-taking propensity to the amount of risk that a bank contributes to the stability of the entire financial system. To do so we we use the CoVaR measure developed by Adrian and Brunnermeier (2016) and the Systemic Expected Shortfall (SES) measure in Acharya et al. (2016) to measure systemic risk. III. Numerical and Empirical Methods We assume that the traditional moral hazard model is an appropriate representation of the contracting problem involving principal and agent. My model is based on a traditional single period agency setting with a risk-neutral principal (i.e., the representative shareholder in theory and the board of directors in reality) and a risk-averse and effort-averse agent (i.e., the CEO). The CEO has an additively separable utility function (CRRA) defined over terminal wealth, the sum of the initial wealth compounded at risk-free rate in one period and the current period compensation: 1 WT UW ( T ), γ 1 1 UW ( ) ln( W), γ = 1 T T The CEO s disutility of the effort, D(e), is a convex and monotonic increasing function of effort e. The CEO selects the effort level to maximize the expected utility of terminal wealth less the disutility. It is assumed that CEO s choice of effort satisfy the incentive compatibility (IC) constraint. The risk-neutral principal selects a compensation contract to maximize the expected value of the firm net of the expected compensation to the CEO. We assume that the compensation contains only cash (salary and bonus), restricted stock and stock options, and the principal decides the allocation of the compensation among these types. We require the 8

9 minimum payment (MP) constraint or limited liability, meaning the cash compensation is greater than or equal to zero. This is consistent with Armstrong, Larcker and Su (2007). It is not a trivial constraint, and it has serious impact on the result of this non-linear optimization problem that we. Dittmann and Maug (2007) allow cash compensation bounded below at CEO s negative initial wealth: W0. Their result has negative cash compensation and zero weight in options, and they in turn argue for all restricted stock grants as optimal compensation. Without the limited liability constraint, the CEOs are forced to invest all their wealth to their company stocks. This is like replicating stock options in discrete time using delta number of stocks. The no-shorting (NS) constraint is that the number of stock and the number of options are positive and the total shares (TS) constraint is that the total number of stocks and options is less than total shares outstanding. It is further assumed that the compensation satisfies the individual rationality (IR) constraint that the expected utility from this compensation contract less the cost of effort is greater than or equal to the utility of the reservation wage that the CEO can earn in the outside the executive labor market. The basic principal s problem is defined as follows. The principal (shareholders) maximizes expected profit, measured as total market value of equity net of compensation paid to the agent (CEO) subject to incentive compatibility (IC) and participation constraint (IR): Max E[ NP ( P max( P K,0)) e], 1, 2, e T 1 T 2 T rt f s.t. e arg max{ E[ U(( W0 ) e 1PT 2max( PT K,0)) e ] D( e )} (IC) e rt 0 f 1 T 2 E[ U(( W ) e P max( P K,0)) e] D( e) U (IR) T 0 (MP) 0, 0 (NS) 1 2 (TS) 1 2 N N is the total number of shares outstanding. α is the cash compensation including salary and bonus. β 1 is the number of restricted stocks granted to the CEO. β 2 is the number of stock options granted to the CEO with strike price K. W 0 is CEO s initial wealth. D(e) is the CEO s disutility of action or effort, e, and U is the CEO s reservation utility. P T is the terminal stock price at time 1, and its distribution is lognormal: PT 2 ( rf ) T u T 2 0 Pe, where u N(0,1). 9

10 Without any assumption of disutility function D(e), the implementation of the model depends on first-order approach which replaces the (IC) constraint with the respective first-order condition for utility maximization by the CEO, by assuming observed compensation contracts imply optimal actions of CEOs. Following the definition of utility-adjusted pay-for-performance sensitivity in Dittmann and Maug (2007): rt f T 0 1 T 2 T W ( W ) e P max( P K,0) The first order condition of the IC constraint: e arg max{ E[ U( W ) D( e )} is: du ( WT ) du dp dd() e E de dp de de UPPS is defined as: 0 [ ] 0 0 du ( W ) dw ( P ) dw ( P ) UPPS e E e E W rt f T T 0 rt f T 0 [ ] [ T ] dwt dp0 dp0 UPPS depends only on the observable compensation contract parameters including W T and γ, but not P 0 (e) and D(e). We further assume that the observed compensation contracts reflect the optimal action taken by that CEO, thus UPPS can be inferred from the observed contract data. In addition to this optimal effort condition, the model assumes that the observed pay structure (i.e., the allocation of executive compensation in the form of salary, stock and options) has already attained the level at the lowest cost to the firm. The degree of riskaversion (Gamma or γ) can be implied by numerically solving the following optimization problem. The level of risk-aversion (γ) at which the principal (shareholders) minimizes the cost of executive compensation subject to incentive compatibility of the agent s choice of effort (IC) and participation constraint (IR) that the agent s expected net utility from the contract is at least as great as his outside option. Min P C s.t. T 1 2 T observed 1, observed 2, observed e UPPS( W (,, )) UPPS( W (,, )) (IC) EUW [ ( (,, ))] EUW [ ( (,, ))] (IR) T 1 2 T observed 1, observed 2, observed observed, 1 1,observed, 2 2,observed P 0 is the stock price at time 0, and C 0 is the call options price estimated by the Black-Scholes formula. T 10

11 The object function is linear; however there is a non-linear constraint, namely the UPPS function. We use the estimation method in Dong (2014) to solve this non-linear programming problem. Basically, the solver applies a sequential quadratic programming (SQP) method which solves a quadratic programming (QP) sub-problem at each iteration, then updates an estimate of the Hessian of the Lagrangian at each iteration using the BFGS formula. Internally, the solver performs a line search using a merit function and the QP sub-problem is solved using the active-set strategy. There is an additional constraint for the optimization that the value of gamma is within the range of 0 to 10. This restriction is based on the findings in prior studies that the degree of risk-aversion is generally smaller than 10 (Arrow 1971; Friend and Blume 1975; Hansen and Singleton 1982, 1984; Epstein and Zin 1991; Ferson and Constantinides 1991; Jorion and Giovannini 1993; Normandin and St-Amour 1998; Ait-Sahalia and Lo 2000; Guo and Whitelaw 2006). Unfortunately, when this constraint is strictly enforced as in the first half of the tests in this paper, many firm-ceo pairs may not have feasible solutions. Because we suspect that this restriction is too strong to be of much use, we will relax it to be within the range of 0 to 20 in the second half of the tests that relate bank CEO risk-taking to systemic risk. After obtaining the implied risk-aversion (Gamma or γ) of individual CEOs, we conduct pooled OLS regression in the following form to study the cross-sectional variation of managerial risk preference in terms of CEO characteristics (e.g., age, non-firm wealth), compensation contract characteristics (e.g., salary, stock grants, option grants, stock ownership and option ownership) and firm financial characteristics (e.g., asset size, financial leverage, market to book, asset turnover, return on equity, stock return, cash liquidity): Gamma CEO Chars Compensation Chars Firm Chars it, 0 1 it, 2 it, 3 it, it, In order to capture systemic risk in the financial sector we use two econometric measures: CoVaR (Adrian and Brunnermeier 2016) and SES (Acharya et al. 2016). CoVaR is the value at risk of the entire financial system conditional on an individual institution in distress. More formally, CoVaR is the difference between the CoVaR, conditional on a financial institution being in distress, and the CoVaR, conditional on its operating in its median state. A number of papers have used the CoVaR measure in various contexts. Brunnermeier, Dong, and Palia (2012) find that banks actively engaged in trading, investment banking and venture capital contributed more to systemic risk and Gauthier, Lehar and Souissi (2012) use it to examine Canadian institutions. Adrian and Brunnermeier (2008) suggest that prudential capital 11

12 regulation should not just be based on the Value-at-Risk (VaR) of a bank but also on the CoVaR, which by their predictive power alert regulators who can use them as a basis for a preemptive countercyclical capital regulation such as a capital surcharge or Pigovian tax. 6 Let CoVaR denote the Value at Risk of the entire financial system (portfolio) system i q conditional on bank i being in distress (in other words, the loss of bank i is at its level of i VaR q ). That is, CoVaR is essentially a measure of systemic risk in the q% quantile of this system i q conditional probability distribution: Probability R CoVaR R VaR q system system i i i ( q q) Similarly, let CoVaR denote the financial system s VaR, conditional on a bank system, i median q operating in its median state (in other words, the return of bank i is at its median level). That is, CoVaR measures the systemic risk when business is normal for bank i : system, i median q Probability R CoVaR R median q, ( system system i median i i q ) Bank i s contribution to systemic risk can be defined as the difference between the financial system s VaR conditional on bank i in distress ( CoVaR system i q ), and the financial, system s VaR conditional on bank i functioning in its median state ( CoVaR system i median ): CoVaR CoVaR CoVaR i system i system i, median q q q q To estimate this measure of an individual bank s systemic risk contribution, i.e., i CoVaR q, we need to calculate two conditional VaRs for each bank, namely CoVaR and system i q CoVaR. For the systemic risk conditional on a bank being in distress ( CoVaR system i ), system, i median q we run a 1% quantile regression using the weekly data 7 to estimate the coefficients i, system i, system i and R system i : Z i i i i t t 1 q i, 6 For detailed discussions of financial institution risk, see Dong and Calluzzo (2015). 7 It should be noted that for each financial institution on average there are three observations for the dependent variable that are in the 1% quantile region given that we have six years of weekly data: =3.12. Similarly, we have this data scarcity issue in estimating 0.1% VAR. This problem of data scarcity occurs when the sample size is not very large and the estimated quantile is low (0.1% and 1%) relative to the size of the data, and the problem is made worse by the presence of control variables and fixed effects. We will address this concern using alternative estimation methods in the robustness check section. 12

13 R Z R system system i system i system i i system i t t 1 t 1 and run a 50% quantile (median) regression to estimate the coefficients where R Z i i, median i, median i, median t t 1 imedian, and imedian, : i R t is the weekly market-value return of bank i at time t and R system t is the weekly market-value return of all N banks ( i j 1,2,3..., N ) in the financial system at time t. Zt 1 is the vector of macroeconomic and finance factors in the previous week, including market return, equity volatility, liquidity risk, interest rate risk, term structure, default risk and real-estate return. We obtain value-weighted market returns from the database of the S&P 500 Index CRSP Indices Daily. We use weekly value-weighted equity returns (excluding ADRs) with all distributions to proxy for the market return. Volatility is defined as the standard deviation of log market returns. Liquidity risk is defined as the difference between the three-month LIBOR rate and the three-month T-bill rate. For the next three interest rate variables we calculate the changes from this week t to t-1. Interest rate risk is defined as the change in the three-month T- bill rate. Term structure is defined as the change in the slope of the yield curve (yield spread between the 10-year T-bond rate and the three-month T-bill rate. Default risk is defined as the change in the credit spread between the 10-year BAA corporate bonds and the 10-year T-Bond rate. All interest rate data is obtained from the U.S. Federal Reserve website and Compustat Daily Treasury database. Real estate returns are proxied by the Federal Housing Finance Agency s FHFA House Price Index for all 50 U.S. states. ˆ i, We predict an individual bank s VaR and median equity return using the coefficients ˆ i,, ˆ imedian and ˆ imedian, estimated from the quantile regressions: VaR Rˆ ˆ ˆ Z i i i i qt, t t 1 R Rˆ ˆ ˆ Z imedian, i imedian, imedian, t t t 1 i After obtaining the unconditional VaRs of an individual bank i ( VaR qt, ) and that bank s asset return in its median state ( R distress ( CoVaR system i q quantile regression: imedian, t ) using the coefficients ), we predict the systemic risk conditional on bank i being in ˆ system i, ˆ system i, and CoVaR Rˆ ˆ ˆ Z ˆ VaR system i system system i system i system i i qt, t t 1 qt, ˆsystem i estimated from this 13

14 Similarly, we can calculate the systemic risk conditional on bank i functioning in its median state ( CoVaR system, i median q ) as: CoVaR ˆ ˆ Z ˆ R system, i median system i system i system i i, median qt, t 1 t Bank i s contribution to systemic risk is the difference between the financial system s VaR if bank i is at risk and the financial system s VaR if bank i is in its median state: CoVaR CoVaR CoVaR i system i system i, median qt, qt, qt, We are interested in the VaR at the 1% confident level, therefore the systemic risk of individual bank at q=1% can be written as: CoVaR CoVaR CoVaR i system i system i, median 1%, t 1%, t 1%, t And according to Adrian and Brunnermeier (2008), this can be simplified to: CoVaR ˆ ( VaR R ) i systemi i i, median 1%, t 1%, t t We obtain the estimates of VaR 0.1% and CoVaR 1% of all individual financial institution for each year from 2005 to 2011 in this first-stage of estimation. Then, in the second-stage, we pool all VaRs and CoVaRs together and estimate a set of panel regression models consisting of the estimated financial institution risks (VaR 0.1% and CoVaR 1% ) of the current period (year) and other firm characteristic variables (market value, financial leverage, log total assets, maturity mismatch, market-to-book, equity return, equity volatility, and VaR) of the previous time period (year). In an attempt to quantify a bank s vulnerability to financial system failures, Acharya, et al. (2016) propose a model-implied measure of Systemic Expected Shortfall (SES) that captures the amount a bank will be undercapitalized by in a systemic event in which the entire financial system is undercapitalized. Instead of focusing on the return distribution of the banking system conditional on the distress of a particular bank as measured by CoVaR, the measure of SES focuses on a bank s return distribution given that the entire financial system is in distress. Adrian and Brunnermeier (2008) refer to this form of conditioning as exposure CoVaR, as it measures which financial institution is more exposed to a systemic crisis rather than which institution contributes more risk to a systemic crisis. In this paper, we estimate a bank s SES at the 5% risk level using daily equity returns. The systemic crisis event is the 5% worst days for the aggregate equity return of the entire banking system in any given year, and the average 14

15 equity return of a bank during these worst market days is defined as this bank s SES at the 5% level. After obtaining both the implied risk-aversion (Gamma or γ) of individual CEOs and the measures of systemic risk ( CoVaR and SES) of individual bank holding companies, we conduct pooled OLS regression in the following form to study the cross-sectional variation of managerial risk preference in terms of CEO characteristics (e.g., age, non-firm wealth), compensation contract characteristics (e.g., salary, stock grants, option grants, stock ownership and option ownership) and firm financial characteristics (e.g., asset size, financial leverage, market to book, liquidity, loan portfolio, etc.): Systemic Risk CEO Chars Compensation Chars Firm Chars it, 0 1 it, 2 it, 3 it, it, In addition, to mitigate the omitted variable problem (i.e., unobserved CEO and firm characteristics), we include firm fixed-effects to exploit the variation over time in our measures of CEO risk-aversion as reflected by the risk-taking incentives embedded in the executive compensation contract. IV. Sample Data The sample consists of 290 CEOs from the Compustat Executive Compensation database during the period of 2003 to This rather small sample size reflects the requirement that these executives have been serving as CEOs for ten years, meaning their compensation contract information must exist in the Executive Compensation database for at least ten consecutive years. The wealth of a CEO is calculated by taking the present value of their 10-year cash pays including salaries and bonuses plus a 15-year annuity equal to 60% of CEO s cash compensation. This estimation is based on the method used by Armstrong, Larcker and Su (2007). The values of stock price and return, dividend yield, common shares outstanding are taken from the CRSP database, firm level financial accounting information is from the Compustat Annual database, and the annual risk-free rate is downloaded from the U.S. Treasury web site. Table 1 shows the detailed definition of all variables used in this research. [Insert Table 1 Here] We require sample data have non-zero values of salary, stock and option holdings, shares outstanding, stock price, Black-Scholes value, volatility, and total compensation in each 15

16 year. Table 2 shows the number of observations, mean, standard deviation, maximum and minimum values of each variable. [Insert Table 2 Here] The average CEO in the sample is 58 years old with $40 million wealth as a result of accumulating his cash compensation during the previous ten years of employment. The average degree of risk aversion implied by the numerical method proposed in this paper is 4.6, and its distribution (probability density) and industry means of this Arrow-Pratt measure of relative risk-aversion are shown in Figure 2. The majority of CEOs, more than half of the sample, are clustered at a lower level of risk-aversion with mean below 4.0 and the others are clustered at a higher level of risk-aversion between 7.0 and 9.0. It is interesting to note that chief executives in wholesale trade industry (5.5) are, on the average, the most risk-averse of all nine industry groups, followed by those in manufacture and mining industries. CEOs in finance, insurance and real estate industries (4.9) rank fourth behind those in retail trade, construction, and agriculture industries in terms of risk-taking. [Insert Figure 2 Here] It is important to note that the value of Gamma is within the range of 0 to 10 due to a constraint that is enforced in the optimization estimation. This restriction is based on the findings in prior studies that the degree of risk-aversion is generally smaller than 10, and we will relax this restriction in the later section. We also plot the relations between the degree of risk-aversion and CEO wealth, age and firm size in Figure 3, 4, and 5 respectively. Besides the fact that riskaversions are centered at two different levels similar to what is shown in Figure 1, these graphs do not suggest a strong association between CEO risk-aversion and personal and firm characteristics. [Insert Figure 3, 4 and 5 Here] An examination of the Pearson s correlation matrix in Table 3 indicates that correlations between independent variables are generally small. This low correlation among the covariates helps prevent the problem of multicollinearity that causes high standard errors and low significance levels when both variables are included in the same regression. However, there is three pairs of variables having correlations above or close to 0.9: Stock Grants and Option Grants (0.91), Stock Grants and Stock Ownership (0.86), and Option Grants and Stock Ownership (0.89). To 16

17 be cautious, in the following cross-sectional analysis of the determinants of managerial risk preferences, we will calculate and report the variance inflation factor (VIF) to assess the severity of multicollinearity in each specification. [Insert Table 3 Here] V. Empirical Results Risk-aversion of CEOs in All Firms The results from the pooled OLS regressions reported in Table 4 suggest that the implied managerial risk-aversion is negatively related to the CEO s non-firm wealth and his stock option s moneyness. However, other personal and compensation characteristics, such as CEO age, wage, current year stock and option grants, and accumulated equity ownership of the firm, and firm financial characteristic, such as size (Total Assts), profitability (ROE), leverage (Book Assets to Equity), current asset liquidity (Cash Holding), stock performance (annual return) and operating efficiency (Asset Turnover) seem unrelated to the degree of risk-aversion. [Insert Table 4 Here] The Variance Inflation Factor (VIF) reported in the table is calculated for each independent variable to determine if these variables display collinearity amongst themselves. The mean VIFs (ranging from 2.5 to 4.1) reported at the bottom of table are below the cut-off point of ten (Myers 2000), suggesting no problem with multicollinearity in our regressions. Based on the significance of coefficient loadings in specifications (1), (2) and (3) we can identify three factors affecting the degree of relative risk-aversion (Gamma or γ) in a statistically significant way: CEO Non-firm Wealth (at 1% and 5% level), In-The-Money of Owned Options (i.e., the call option s moneyness, at 1% and 5% level), and the firm s Financial Leverage (at 10% level). A useful way to look at the economic significance of the ability of these determinant factors to affect managerial risk preference is to examine the percentage change in risk-aversion level when the value of one of these variables is increased by one standard deviation. We estimate the magnitude of the economic effects for three specifications and report them in Table 5. [Insert Table 5 Here] The predicted percentage change in relative risk-aversion (Gamma or γ) that our regression models generate in response to one standard deviation shock to the CEO s non-firm 17

18 wealth is -5.1%, -3.9%, and -4.0% for regression specifications (1), (2), and (3) respectively. Similarly, the changes in managerial risk-aversion are -3.5% and -8.7% in response to one standard deviation change in the CEO s option portfolio moneyness and the firm s financial leverage. These results are robust to perturbation of study variates and methods in estimating the degree of risk aversion by calculating CEO wealth using 5-year income data and by adding [-10%,+10%] random disturbance to the values of individual wealth, wage, stock grants, option grants, stock ownership, option ownership, and in-the-money of options. We create a new sample by requiring CEO compensation contract information exist in the Executive Compensation database for at least five consecutive years rather than ten consecutive years as in the previous results. [Insert Table 6 Here] The summary statistics in Table 6 show that not only the sample size is larger but also the estimated level of risk aversion (5.1) is slightly higher than the one obtained in the previous results (4.6). We repeat our pooled regression analysis using this new data set and the coefficient estimates are reported in Table 7. In addition to the negative effects of CEO wealth and option in-the-money, a CEO s risk-aversion is positively related to her stock grants and the firm s financial leverage and negatively related to her option ownership and the firm s size (total assets), market-to-book, and asset turnover. [Insert Table 7 Here] In the next robustness check, we add [-10%,+10%] random disturbance to the values of individual wealth, wage, stock grants, option grants, stock ownership, option ownership, and in-the-money of options and re-estimate the degree of CEO risk-aversion. The summary statistics in Table 8 and regression results in Table 9 are similar to the ones obtained in the previous robustness test. [Insert Table 8 and Table 9 Here] Risk-aversion of Bank CEOs and Systemic Risk To understand the relationship between the degree of risk-taking of a bank CEO and the amount of contagion risk that the bank contributes to the entire financial system, we regress the 18

19 level of systemic risk on the measure of CEO s risk-aversion along with other control variables. Table 10 shows the summary statistics of this rather small sample that only includes CEOs of bank holding companies. [Insert Table 10 Here] Still, the sample size (N=561) is larger than that of the first sample (N=290) in Table 2. The reason is due to two relaxed constraints in sample construction and numerical estimation. The first one is the elimination of 10-year tenure requirement in the same firm. Instead, we use the future value of 10-year annuity payment formula to calculate the initial non-firm wealth of the CEO where r is the average annual interest rate, CF is approximated by the total compensation in dollars in including salary, bonus and, restricted stock and stock options : Ordinary Annuity (1 10 r) 1 r FV CF The second relaxed constraint is the requirement that the value of Gamma is within the range of 0 to 10. Unfortunately, when this constraint is strictly enforced as shown in the first half of the tests in this paper, many firm-ceo pairs may not have feasible solutions. Because we suspect that this restriction is too strong to be of much use, we will relax it to be within the range of 0 to 20 in risk-aversion estimation. The average CEO age (58 year-old) and initial non-firm wealth ($40 million) in this bank CEO sample are similar to those in the previous two samples. The average implied-risk aversion is 15 and this is larger than that of previous findings is due to the relaxed restriction on the range of Gamma (0 to 20). The first two cross-sectional muntivariate tests are based on pooled OLS regression with year fixed-effects. The specifications in Table 11 have CoVaR as the measure of a bank s systemic risk on the LHS and the Gamma, the degree of risk-aversion of bank CEOs, on the RHS. The finding is somewhat surprising: after controlling for CEO and bank characteristics (e.g., age, wealth, wage, stock grants, option grants, stock ownership, option ownership, option moneyness, the natural logarithm of total assets, financial leverage, market to book, liquidity, return on asset, annual stock return, loan portfolios, and loan commitment), the risk-taking incentives embedded in the compensation contract of a bank CEO is not related to the amount of contagion risk that this bank contributes to the banking system, Although the signs of Risk-Aversion are negative, they not statistically significant in all regression specifications. 19

20 [Insert Table 11 Here] The regressions in Table 12 use SES as the measure of a bank s systemic risk, proxying for the vulnerability of a bank to the financial stability of the entire banking system, on the LHS and the Gamma, the degree of risk-aversion of bank CEOs, on the RHS. Again, there is no statistical association between these two variables, suggesting that a risk-taking CEO of a bank holding company is not necessarily make the bank vulnerable to contagion risk. [Insert Table 12 Here] While the evidence presented thus far is convincing, it is still possible that the omitted variable problem (i.e., unobserved CEO and firm characteristics) may have biased the coefficient estimates. In the following two tests we include firm fixed-effects, in addition to year fixedeffects in the previous regression specifications, to exploit the variation over time in our measures of bank CEO risk-aversion as reflected by the risk-taking incentives embedded in the executive compensation contract. The basic specifications in Table 13 and Table 14 are same as the ones in Table 11 and Table 12 respectively, except including the bank fixed-effects. The insignificant coefficient estimates of Risk-Aversion remain in both tables, suggesting that even the risk-taking incentives increase in the compensation contract, they do not necessarily increase the contagion risk of the bank. [Insert Table 13 and Table 14 Here] Finally, it is noted in Dittmann and Maug (2007) that the calibration of a principal-agent model using observed data is sensitive to the CEO s non-firm wealth, which is often not observable, and each of the two estimation methods of CEO wealth presented in this research has its limitations. In the first method, the requirement of 10-year or 5-year continuous compensation data of a CEO in the Execcomp dataset reduces the sample size. It is often the case that some of them left the sample and then reappeared in a later year. In the second method, whereas the use of 10-year annuity payment formula based on one-year income data (cash flow in the initial year) helps increase the sample size, it has to assume that future incomes do not fluctuate over time. Therefore, as a robustness check, we combine both estimation methods to create a simple two-stage method to predict CEO wealth. In the first stage, we conduct a pooled OLS regression on a sample of CEOs with 10-year accumulated wealth (from 20

21 the first method) to estimate the relationship between the 10-year accumulated wealth and the cash flow in the initial year (used in the second method): Wealth Cashflow Age it, it, it, t it, In the second stage, we use the coefficient estimates (α, β, γ, and λ) and the income cash flow and CEO age in each year in the larger sample (for the second method) to predict a CEO s wealth: Wˆ ˆ ˆ CF ˆ AGE ˆ it, it, it, t it, After obtaining the fitted wealth, we repeat the regression models in Tables 13 and 14. Overall, the insignificant coefficient estimates of risk-aversion shown in Tables 15 and 16 confirm our previous findings that risk-taking preference of bank CEOs is not related to the bank s systemic risk measured in both CoVaR and SES. [Insert Table 15 and Table 16 Here] VI. Discussion and Conclusion Fitting a principal-agent model using observed executive compensation data produces a number of insights that have not been presented in the empirical corporate finance literature. We find a very low degree of risk-aversion among CEOs with the average Arrow-Pratt measure of relative risk-aversion (CRRA) being 4.6 for 290 managers who have served as CEOs for more than ten years. This result is, to some extent, consistent with the theoretical finding in the previous studies. For example, Hemmer, Kim and Verrecchia (2000) use a principal agent model to show that in the case of log utility, if relative risk aversion is less than one, the optimal contract is convex in stock value. The assumptions behind our numerical estimation method are optimal effort and optimal pay. The first one means that when a manager accepts the offer of employment to become or continue to serve as the CEO of the firm, the compensation contract reflects the optimal level of efforts that the CEO will and must exert in order to maximize the firm value. The optimal pay assumption suggests that the observed compensation contract offered by the firm has already attained the level at the lowest cost to the firm. To better understand the cross-sectional variation of managerial risk preferences, we study the determinants of the model-implied risk-aversion by conducting pooled OLS 21