Corporate Governance and Risk-Taking Incentives

Corporate Governance and Risk-Taking Incentives

Marina Ciobanu

University of Groningen

Faculty of Economics and Business

Supervisor Prof. Dr. R.E. Wessels

June 2016

Abstract

This study analyzes the relationship between risk-taking incentives embedded in the CEO compensation package and firm risk profile, for a sample of 83 US commercial banks. Using a simultaneous system of equations to account for the endogenous causal relationship between CEO risk incentives and bank risk profile, I find empirical evidence on the significant positive relationship between Vega, measure of risk-taking incentives, and total bank risk, measured by daily stock return volatility.

Keywords: Corporate Governance, Risk-taking Incentives, Firm Risk, Banking

Industry

I. Introduction

Most of the previous literature on corporate governance and managerial compensation choose to exclude banks and other financial institutions from their sample, when investigating the relationship between equity incentives and risk-taking. Some authors like Adams and Mehran, 2003, motivate this decision by claiming that equity compensation is less important in banking industry because of the highly regulated nature of the industry. But studies investigating bank managerial compensation after deregulation, Riegle-Neal Interstate Banking and Branching Efficiency Act of 1994 and the Gramm–Leach–Bliley Act (GLBA), also known as the Financial Services Modernization Act of 1999, observed a significant increase in the proportion of equity compensation in the bank executive pay package, DeYoung et al., 2010. Therefore, equity compensation through, restricted stock grants and executive stock options (EOS), is an important part of CEO compensation package in banking industry too, and investigating how it affects the risk profile of the bank is a matter of interest, especially, in the context of the recent financial crisis.

Speaking about the recent financial turmoil, there are many economists who share the view that “Wall Street bankers are those to be blamed” of the financial crisis of 2008. Even though most of the studies investigating this question concluded that CEO compensation cannot be held responsible for the recent financial collapse, banks managerial remuneration structure was highly criticized and considered to be partly responsible for the risk-taking incentives that led to such a high risk exposure of major financial institutions, at the beginning of third quarter of 2007.

equations to account for the endogenous variables problem, very common in corporate governance studies. Therefore, I analyze the relationship between CEO incentives and risk profile taking into account that, because of omitted variables, errors in variable measurement or causal relationship, the error term of the regression is not independent, but correlated with the explanatory variables. In order get consistent and unbiased results, a great part of this analysis is concentrated on the endogeneity issue, its implications on the validity of the study and how to deal with it. Following the steps to correct for this issue, I find empirical evidence on the significant positive effect of equity executive incentives on total risk of the bank, but no significant evidence on the impact on systematic measure of risk.

This paper contributes to the paucity literature on executive compensation and firm performance, within financial institutions by bringing empirical evidence on the positive causal relationship between firm risk profile and CEO equity compensation incentives. Also, it sheds some light into the factors of CEO compensation structure and incentives.

II. Theoretical Framework

Most of the literature on corporate governance and executive compensation is extensively based on the agency theory framework, under which shareholders own the firm and act as principals by delegating board directors and executives as their agents in managing the company under shareholders' best interests. According to Jensen and Meckling, 1976, the fundamental possible conflict, when principal delegate a great amount of decisional sway to his agent, is that if both participants are utility maximizers, the agent will be prone to not always adopt the best decisions that will benefit the principal. Under utility maximization is implied that both owners and managers of the company are individuals that act in their self-interest to fulfill their own desires and aspirations. Conflicting with the view of a perfect agent, that manages the company in the same manner the shareholders would if they had the required skills and expertise, the executives might adopt strategies suiting their own career and life plans instead of those of the firm and its capital providers. Therefore, firm management is examined under this framework to acknowledge the existent principal-agent problem and to propose ways of mitigating it.

interests with the firm owners interests, thus inducing him to behave more towards firm's benefit. Given the ownership dispersion, the relative high costs of monitoring and the legal framework in the majority of states in US, monitoring is not considered a feasible and effective method to deal with the agency problem arising on the executive level. Setting right incentives through compensation terms seems to be a more convenient method of aligning the interests of both top management and shareholders, in maximizing firm value. Though not perfect, since as stated by Core and Guay, 2005, incentive alignment between shareholders and their agents will always be followed by some degree of shortcoming. Even though, a great amount of literature recognizes the agency problem between boards and shareholders of the firm, in this study, I focus on the executive incentives as instrument in mitigating the agency problem between CEO and bank shareholders. In US and majority of corporations around the world, the responsibilities of appointing, supervising, designing compensation packages and departure of the executive team, CEO included, are delegated to the board of directors. Thus, being in charge of setting the top management compensation plan, boards play an essential role in embedding the right executive incentives.

So far, from the agency theory outlook the essential question concerning executive compensation is "How well do executive compensation packages achieve to align top management and shareholders' interests via embedded incentives, leading to shareholders wealth growth?". Incentives are strong factors that may considerably influence human behavior and are extensively used in present-day society, but sometimes they can be too powerful and even misleading, that's why cautiousness is required when using them.

Executive incentives and risk taking

penalty for a fall in stock price. Consequently it might induce way stronger risk-reducing incentives.

EOS are call options, since they give the executive the right to buy firm shares at a predetermined contractual price (exercise price), after an elapsed period of time (option expiration date). Because of the attached vesting period, executive stock options fall into the exotic options category. Contrary to restricted stocks, that have a relatively linear payoff structure, EOSs have a more complex design, and their specific nonlinear payoff structure is considered to be the major element in inducing risk-taking incentives, Kolb, 2012. Most of the studies on executive compensation analyze the emerged equity incentives relying on the assumption that the shareholder is neutral and the executive, CEO in this case, is an risk-adverse manager, whose wealth is strongly tied to the firm value. Studies like Haugen and Senbet, 1981, Smith and Stulz, 1985, point out that using EOS as compensation for risk-averse executives, will stimulate them to undertake riskier positive net present value projects, since, the expected payoff from this type of compensation is increasing with the volatility of the underlying stock returns. Anyway, authors like Carpenter, 2000, Ross, 2004, Lewellen, 2006, claim that under constant relative risk aversion (CRRA), option compensations does not all the time induce risk-taking behavior, mainly, because the manager has a fixed volatility bound for his own portfolio of options. Increasing the number of awarded EOS leads to a more volatile personal portfolio that could be counterbalanced through lowering the underlying stock volatility.

simultaneous increase in Delta amplifies his aversion to firm risk, because of the possible value implications of a decrease in stock price to his personal firm-specific portfolio.

Executive Incentives and Implications on Bank Risk

and investigating the relationship between risk-taking incentives (Vega and Delta) and level of risk is a matter of interest, especially, in the context of the recent financial crisis.

III. Research Design

One of the most prevalent and serious issues of corporate finance studies is endogeneity, which mainly implies that the explanatory variables and the error term of the regression are correlated. Therefore, by violating the exogenous assumption of explanatory variables, the parameter estimates are no longer unbiased and consistent and OLS is not a consistent estimator anymore. Errors in variables measurement, omitted variables and simultaneous causality are the three sources of endogeneity, recognized and elaborately described in the paper of Roberts and Whited, 2012. As explained in the book of Wooldridge, 2002, the omitted variables bias is related to variables that influence the dependent variable and are correlated with one or more of the explanatory variables, but which where, for some reason, not included into the regression specification. Therefore, the error term contains part of the variation explained by these omitted variables and is, consequently, correlated with one or more of the explanatory variables. Omitted variables are a common problem in the corporate finance empirical studies, mostly, because it is very difficult to observe and quantify all the dimensions that affect each individual firm or CEO. Measurement error problem emerge when the real value of the variable is unobservable and there are some disparities between the true value and the observable proxies used in the regression. Thus, the unobserved effect of the dependent variable, subject to measurement errors, becomes part of the regression disturbance term. As argued by Roberts and Whited, 2012, measurement errors do not always lead to attenuation in the biasness of the estimated coefficients, but when it is correlated with the imperfect proxy variable or other explanatory variable from the equation, the regression error term is no longer uncorrelated with the used explanatory variables. Simultaneity bias arises when there is a causality relationship in both directions between dependent variable and explanatory variable. Because of the simultaneous causality, OLS estimation picks up effects from both directions and the regression error term is correlated with the explanatory variable, therefore leading to biased and inconsistent coefficient estimates.

with the error term. In the last ten years, researchers in corporate finance and managerial compensation have been aware of the causes of endogeneity when building models to investigate the relationship of executive incentives and firm risk and performance. According to Hamilton and Nickerson, 2003, strategic management is essentially built on the conception that decisions are not randomly done, but founded on the expectations of how firm performance responds to them. So, in the setting of this study, it can be considered that boards of directors take into consideration the expected or desired performance outcome when setting risk-taking incentives through CEO compensation, and there is a simultaneous causality relationship between bank risk and CEO incentives. However, few studies like Coles et al., 2006 and DeYoung et al., 2010 approached the causality aspect of the relationship. Most of the literature is focused on only one of the directions of the relation. While Low, 2009, Hagendorff and Vallascas, 2011 and Gregg et al., 2012 explore the influence of Delta and Vega on the risk level of the firm, studies like Álvarez-Díez et al., 2013, Rajgopal and Shevlin, 2002, investigate the effect of stock return volatility on CEO wealth sensitivity to changes in stock price, Delta, and CEO wealth sensitivity to changes in stock return volatility, Vega.

Besides the simultaneous causality, other sources of endogeneity that might have serious implications on the validity of this analysis are omitted variables and measurement errors. As explained further in the data section, I use the, widely employed in previous literature, standard Black–Scholes (1973) option pricing model (BS) to calculate Delta and Vega, as managerial incentives. Nevertheless, recognizing that specific measurement errors of delta and vega are present and might be correlated with the explanatory variables can help in dealing with the endogeneity issue. Accounting for all the determinants of each firm risk and managerial incentives is impossible and omitted variable bias might be present in the OLS coefficient estimates if Delta and Vega are correlated with the excluded determinants.

endogeneity problem is the use of instrumental variables, (Murray, 2006, Bascle, 2008, Roberts and Whited, 2012). Estimation methods using instrumental variables center on the variation of the endogenous variable that are not correlated with the error term ignoring the variations that are correlated and might bias the coefficients estimates. In order for a variable to be considered a valid instrument it needs to satisfy two conditions, referred as the relevance and exclusion conditions (Roberts and Whited, 2012). The relevance condition presumes that the partial correlation between the instrumental variable and the endogenous variable is different than zero, which can be empirically tested from the first stage regression results, when using two stage least square (2SLS) estimation method. The second condition involves no correlation between the instrumental variable and the error term of the structural equation. Basically, it implies that the instrumental variable does not have a direct impact on the dependent variable and the only way it affects the dependent variable is through its effect on the endogenous explanatory variable. Unlike the relevance condition, the exclusion condition cannot be tested since the regression error term is not observable. Moreover, based on the argument of Murray, 2006, the most important factor in supporting the validity of an instrument is a strong theoretical reasoning on how the instrumental variable interacts with the endogenous variable.

To address the endogeneity issue, that might threat the internal validity of the analysis, I employ a instrumental variables estimation method using a simultaneous system of three equations for risk, Delta and Vega. Risk equation has one and Vega and Delta equations have, each, two specific explanatory variables that are used as instrumental variables, when estimating the other two system equations.

In order to be able to account for different specific economic conditions faced by each commercial bank based on the states in which they operate in, I use in the risk equation (1) a variable EconCond computed following the method of DeYoung et al., 2010. The economic conditions faced by the depositors of a bank have clear implications in the welfare of a bank

(1)

(2)

and, consequently, on how risky the institution is perceived by the investors. The economic conditions variable is the sum of products of the Federal Reserve Bank of Philadelphia’s Coincident Index for each state and the percentage of total deposits of each bank, raised in that specific state. The Coincident Index for each state implies a combination of four state-level indicators and presents the current economic conditions with a single indicator. The state-level components for every coincident index are nonfarm payroll employment, average hours worked in manufacturing, the unemployment rate, and wage and salary disbursements deflated by the consumer price index (U.S. city average)1. Based on the underlying construction principle of this variable, there should be no reason to expect a direct relation with the measures of CEO incentives, Vega and Delta.

The choice of instrumental variables for Vega and Delta are according to previous literature on managerial incentives. Core and Guay, 1999 argue that restricted stocks and stock options are frequently used by cash constrained firms to replace part of the cash managerial compensation. On the other hand, Jensen, 1986 and Stulz, 1990 find evidence that firms with greater cash balances face bigger agency problems, that risk-taking incentives can diminish. Following Core and Guay, 1999 and Armstrong and Vashishtha, 2012, I use the cash and short term investment to total assets as determinant in Vega equation. Another instrumental variable that I use as explanatory variable for the CEO wealth sensitivity to changes in stock return volatility (Vega) is the previous period stock return, which might be used as indicator of firm past performance that the CEO can be rewarded for with EOS. Albeit, there are many studies that claim on the negative relationship between stock returns and future return volatility, Black, 1976 and further studies like Christie, 1982 have explored the ‘‘leverage effect’’ view, that presumes that higher volatility in stock returns comes from the reduction in firm's equity value while the debt level stays unchanged, hence through the increase in leverage of the company. Since I control for the effect of leverage, there should be no concern about a direct relationship between banks past performance variables and the current measures of risk.

In the case of delta as measure of risk-aversion incentives in executive compensation plan, I use natural logarithm of cash compensation and number of years of Chief Executive Officer position as instrumental variables. According to Guay, 1999, cash compensation, salary plus annual bonus, may be used as a proxy for the CEO wealth outside the firm that can decrease the level of executive's risk-aversion. Therefore, greater risk-aversion incentives,

1

Delta, might be needed to control the risk-taking choices of the CEO and a positive relationship between cash compensation and CEO wealth sensitivity to changes in stock price (delta) is expected. Tenure is considered to be an indicator of CEO ability and talent and it helps reduce the uncertainty of firm board towards level of equity incentives to be incorporate in the compensation scheme, and as CEO retirement is approaching greater equity incentives may be used to countervail possible horizon problems, Core and Guay, 1999. Previous papers like Coles et al., 2006 and DeYoung et al., 2010 used tenure as determinant of delta and found a positive relationship between these two variables.

Total Risk Vega and Delta

Vega, measuring the sensitivity of CEO’s wealth on the volatility of stock returns, is the main equity incentive inducing risk-taking behavior of CEO. Thus, based on this and previous empirical research, it is expected to have a positive significant impact on the total risk of the firm. Regarding Delta, the literature is quite divided: DeYoung et al., 2010, study results show a positive, but insignificant impact of Delta on total risk and a significant negative influence on systematic risk; on the other side, Coles et al., 2006 and Armstrong and Vashishtha, 2012, come to a positive, highly significant coefficient for Delta both for systematic and total risk. Therefore, I do not have a precise expectation on the direction of this relationship. To solve for the high skewed distribution to the right of Delta and Vega, I employ the natural logarithm of the CEO wealth sensitivity measures, rather than the unchanged values.

Concerning the impact of firm risk profile on the CEO equity incentives, equation (2) and (3) try to establish how risk level of the firm influence the structure of CEO compensation and use of risk-taking incentives. Consistent with DeYoung et al., 2010 reasoning, both positive and negative direction on the relationship would provide evidence on the use of managerial compensation incentives to induce or diminish risk-taking behavior of CEO. Furthermore, Rajgopal and Shevlin, 2002 consider that if CEO holds some private information concerning a possible risky but highly valuable investment opportunity, he may influence the compensation committee in establishing higher risk incentives.

higher Vega (higher Delta) compensation contracts are complemented by higher Delta (higher Vega) to better align the interests of both, CEO and shareholders.

Control Variables

The choice on the control variables is according to the revised papers on firm risk and managerial risk-taking behavior. Natural logarithm of total assets, Tassets(ln), is used to account for bank size, since studies of Low, 2009; DeYoung et al., 2010; Álvarez-Díez et al., 2013 came to a negative relationship between firm size and measures of risk. According to Smith and Watts, 1992, executive compensation tends to increase with the size of the firm. Vega and Delta, measuring the CEO's wealth sensitivity to stock price and volatility, are a major element in the executive compensation strategy and should, as a result, be positively influenced by size. Consistent with previous papers (e.g. DeYoung et al., 2010; Armstrong and Vashishtha, 2012) I use the same variable, natural logarithm of total assets, in equations (2) and (3) to control for different bank size.

The firm-specific investment opportunities are also a factor of influence for the total risk, since banks with a greater investment-opportunity set can undertake riskier projects than those with smaller investment-opportunities, (Guay, 1999). I use the natural logarithm of book-to-market ratio. MBratio(ln), to account for this factor. Based on contracting arguments that executives of firms with more growth options are paid more because of their higher marginal product, Smith and Watts, 2003 bring evidence of a positive relationship between investment-opportunity set and managerial compensation. Core et al, 2003 argue that executive equity incentives are also positively related to growth opportunities. Therefore, the natural logarithm of market-to-book ratio variable is present in Vega and Delta equations, to account for different bank investment opportunities.

more recent research of Coles et al., 2006 and DeYoung et al., 2010 show leverage, as measure of riskier policy choices of the firm, to be positively related to Vega and negatively to delta. Following the study of DeYoung et al., 2010, I use the ratio of equity to total assets,

EQratio, to account for different financial leverage and policy choices across banks under

study. Therefore, high EQratio would indicate a less levered bank and low rate-a more levered institution.

To come to an appropriate estimation model, I follow the Bascle, 2008, "road map", presented in the Appendix, Fig. A.2, on how to address endogeneity. I start by estimating each equation using two stage least squares (2SLS) estimation method, specifying the endogenous variables (Total risk/Systematic Risk, Vega(ln), Delta(ln)) and the equation specific instrumental variables. Then, I perform specification and instrumental variables tests that are presented in the results section of the study.

IV. Data

The sample under analysis is formed by merging data from three main sources; bank financial data was collected from Compustat Capital IQ, Execucomp provides data on annual executive compensation plan and bank stock information is available on Center for Research in Securities Prices (CRSP) database. Also, I use historical data provided by Federal Reserve Board website on annual treasury constant maturities, and data on State Coincidence Index from Federal Reserve Bank of Philadelphia. The final sample is composed by 837 CEO/bank observations for the period 2004-2014, from 83 US commercial Banks and 153 different CEO, Table 1 shows the number of observations per year of analysis.

Executive Equity Incentives

I use the February 2016 version of Standard & Poor’s Execucomp database to get executive annual compensation of US commercial banks, (industry SIC code 6020) that were active during the proposed study period, 2004-2014.

Most of the literature has used the standard Black–Scholes (1973) option pricing model (BS) to calculate Delta and Vega, as managerial incentives, but there are few studies like the one of Álvarez-Díez et al., 2013 that used an employee stock options pricing model, implemented by the Cvitanic, Wiener and Zapatero in 2008, which takes into consideration some employee stock options characteristics as the long-term maturity of ESOs, the vesting period restricting the exercise and early exercise. Since these characteristics might differ considerably for each bank and requires detailed information on executive compensation agreements, I use the Black–Scholes model which was widely explored and there are clear methodologies on how to use it in calculating values of delta and vega.

Tabel 1 Data Structure

The table presents the number of observations for each year under analysis. For 2004, 2005, 2006, there is no executive or director compensation information for 31, 32 and 13 banks under investigation. This is most probably related to the SEC Amendment No. 33-8735 on the disclosure requirements for executive and director compensation on October 2004 with effective day on November 7, 20062. Year Nr. of CEO observations 2004 52 2005 51 2006 70 2007 83 2008 83 2009 83 2010 83 2011 83 2012 83 2013 83 2014 83 Total 837

Because of 2006 changes in Execucomp data reporting, based on new accounting regulations introduced by the Financial Accounting Standards Board (FASB) and broadened compensation disclosure requirements of the Securities and Exchanges Commission (SEC), the calculation of Delta and Vega needs to be performed based on two methods; For the 2004-2005 year period, Delta and Vega was computed following the "one year approximation"

2

methodology of Core and Guay, 2002, using information provided by Execucomp for the period prior to 2006 and the method developed by Coles et al., 2006, using data on executive annual compensation from 2006 to 2014.

To check the consistency of the Delta and Vega outcomes, I compare the values of my estimates on executive incentives with those of Coles et al., 2010. Table 2 describes the available estimates in the literature and shows a correlation for the intersection of my estimates on Vega and Delta with the ones of Coles et al., 2010 for 2756 observations on 732 executives, for the period 2004-2010 of 97.76% (98.51%). Following DeYoung et al.,2010, I winsorize Vega and delta at 1st and 99th percentiles of their sample distribution to get rid of possible outliers.

Tabel 2 Estimates of Vega and Delta

Estimate source This research Coles et al., 2010

Period 2004-2014 1992-2010

Nr. of companies 83 3123

Nr. of Executives 1008 39347

Industry Banks Banks and Non-banks

Country US US

Model used Black–Scholes Black–Scholes

Correlation (vega)⃰ 0.97763 Correlation (delta)⃰ 0.98509

⃰ - Correlation for the intersection of my estimates on vega and delta with the ones of Coles, Daniel, and Naveen, 2010 for 2756 observations on 732 executives, for the period 2004-2010.

Bank Risk Profile

Consistent with previous research, I use the standard deviation and market beta of daily stock returns as measures of total risk of the bank. While some studies like Chen et al., (2006), Coles et al., (2006), DeYoung et al., (2010), use the daily stock return volatility as risk measure, Jin, (2002), Sanders and Hambrick (2007) and Álvarez-Díez et al., (2013) follow the method of Carpenter, (1998) in using the 60 monthly observations to construct their risk measure.

betas get higher, respectively their systematic risk increases. Thus, since executives are the ones coordinating the bank day-to-day operations and regulators are concerned about banking system stability, systematic risk is a matter of concern when designing managerial compensation and can be used as measure of risk in the estimation model of this study. I use market beta of daily stock returns to measure the systematic component of total risk.

Descriptive Statistics

Descriptive statistics for all variables used in this analysis are presented in Table 3. There are 837 observations for each variable with the exception of one year previous stock returns (Return(t-1), because only 836 bank from the sample were publicly traded in 2003. Vega has a mean (median) of $131.3155 ($24.5453), and Delta has a mean (median) of $374.5091 ($96.392). Therefore, with any 0.01 increase in stock volatility, the value of equity portfolio of the average bank CEO grows with about $131.3155, and with $374.5091 for each 1% increase in stock price. The time the average bank CEO from the sample has been in his/her position is 9 years and the average total annual compensation he/she gets is 4.199 million, where, approximately, 53.48% comes in form of equity compensation (restricted stock grants and EOS), and 46.52% in form of salary plus annual bonus. Bank size measured by total assets varies considerable across sample; the median size is $10.4 billion, while the 10th percentile ($2.956 bill.) is almost $138 bill. apart from sample's 90th percentile(141.041 bill.), all values measured in 2016 dollars.

Analyzing the average structure of CEO compensation, decomposed by year in Table 1 in the Appendix, it can be observed that despite a slight decrease during financial crisis, equity compensation proportion of total annual compensation has raised significantly since 2004 (47.95%) to 2014 (62.98%). At the same time, looking at the evolution of average CEO Vega and Delta depicted in Fig.A1, there can be observed a decreasing trend in both Delta and Vega values until 2011, when CEO Delta starts raising again, while Vega continues to be relatively small. This could indicate that after 2010, banks board started being more reticent with the level of risk-taking incentives embedded in the CEO equity compensation.

Tabel 3 Summary statistics for risk measures, firm characteristics and CEO compensation characteristics.

Obs Mean Std. Dev.

10th Percentile 50th Percentile 90th Percentile Risk measures Total Risk 837 0.02464 0.01643 0.01094 0.01799 0.04896 Systematic Risk 837 1.31856 0.39936 0.90119 1.24882 1.78483 Firm characteristics

Total Assets ($ mill) 837 90,065.96 313,448.50 2,956.25 10,400.67 141,041.70 Total Assets (ln) 837 9.61954 1.56657 7.99168 9.24963 11.85681 MB ratio 837 1.64008 0.81950 0.75844 1.46605 2.74541 MB ratio(ln) 837 0.37096 0.52174 -0.27392 0.38346 1.00993 Economic Cond 837 156.2612 18.4919 137.5302 153.0168 180.1895 EQratio(t-1) 837 0.09701 0.02427 0.06895 0.09635 0.12519 Return(t-1) 836 0.00041 0.00126 -0.00103 0.00045 0.00184 Return(t-2) 834 0.00030 0.00122 -0.0012 0.00033 0.00168 ROA(t-1) 837 0.00759 0.01250 -0.00117 0.00975 0.01594 Cash Balance/Total Assets 837 0.05010 0.05897 0.01551 0.03079 0.09449

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [1] Total Risk - [2] Systematic Risk 0.651 - [3] Vega(ln) -0.066 -0.031 - [4] Delta(ln) -0.339 -0.242 0.363 - [5] CEO tenure -0.077 -0.071 -0.045 0.299 - [6] Total Assets(t-1,ln) -0.055 0.050 0.243 0.424 -0.124 - [7] MBratio(t-1,ln) -0.350 -0.328 0.178 0.362 0.061 -0.200 -

[8] State Coincident Index -0.055 -0.098 -0.136 -0.010 0.204 -0.080 -0.037 -

[9] Cash Compensation(ln) -0.211 -0.091 0.166 0.390 0.036 0.524 -0.002 -0.078 -

[10] EQratio(t-1) -0.263 -0.131 -0.085 0.006 0.061 -0.039 -0.136 0.161 0.007 -

[11] Return(t-1) -0.394 -0.144 -0.012 0.142 0.020 -0.004 0.302 0.087 0.171 -0.083 -

between Total risk, measured by stock return daily volatility, and Systematic risk, measured by stock market beta. The strong correlation is quite obvious, but it doesn't have any implication on the model. Despite the fact that, theoretically, high Vega and high Delta remuneration plan imply distinct incentives to the CEO, both natural logarithm of Vega and Delta have a negative pair wise correlation coefficient with both measures of risk, total and systematic. This may indicate that when designing compensation plans with strong incentives, Vega and Delta are used in a complementary manner in order to induce the executive in the right direction. Even though, no conclusion can be drawn from simple pair wise correlation coefficients they can shed some light on the relationship between CEO incentives and company risk profile.

In line with the specific business model and type of operations, banks activity and, consequently, banks financial characteristics cannot change too much form year-to-year and autocorrelation might be a matter of concern for the cross-sectional analysis employed in this study. To deal with this issue, I estimate the three equation system using robust clustered, on firm level, standard errors. Standard errors reported in a typical regression imply that each observation is independent within the data set and are, generally, underestimated. Allowing for correlation within each bank data series through cluster analysis, inflate the standard errors, but increase the confidence interval of the estimations.

V. Results

strong theoretical reasons to suspect the endogenous relation between Delta(ln), Vega(ln) and the measures of bank risk, a test of whether endogeneity is present and OLS estimations are inconsistent is necessary. Therefore, I perform, for each equation under the model, the Durbin-Wu-Hausman and Wu-Hausman tests of orthogonality conditions, also called "endogeneity" tests, results are presented in Table 5. When using daily volatility of stock returns(Total Risk) as measure of bank risk profile, the null of exogenous variables is rejected at 1% significance level, indicating that OLS is inconsistent and IV estimation methods are required to account for the correlation between the endogenous explanatory variables and regression error term. Surprisingly, in the case of Systematic Risk, the null of exogenous Vega and Delta variables cannot be rejected under both tests which indicates that OLS estimation method is preferred. Therefore, I proceed by estimating the model using IV 2SLS, when bank risk profile is measured by daily stock returns volatility(Total Risk) and pooled OLS estimator in the case of market beta(Systematic Risk).

Table 5

This table displays the results of tests for endogeneity in IV estimation. The null, H0: variables are exogenous, imply that OLS estimator should be used, since it is consistent and fully efficient. Under both tests the null hypothesis is rejected, OLS estimator is inconsistent and estimation methods accounting for endogenous variables should be used

Tested of endogeneity of , , , Durbin-Wu-Hausma chi-sq (2) test 33.91217 12.28548 4.19064

0.0000 0.00215 0.0123

Wu-Hausman F(2, 825) test 17.4834 6.1598 2.0807

p-value 0.0000 0.0022 0.0126

The Pagan and Hall (1983) and Arellano and Bond (1991) test results indicate that heteroskedasticity and serial correlation are present. Therefore, to account for heteroskedasticity and cross-sectional correlation, I estimate each of the system equation using robust clustered, on firm level, standard errors. By employing cluster standard errors, the assumption of zero correlation across groups still holds while allowing for within-group correlation, on firm level, and increasing the confidence interval of the coefficient estimates.

Total Risk and CEO incentives

exclusion conditions. And, as stated by Murray, 2006, the most important factor in supporting the validity of an instrument is the strong theoretical reasoning on how the instrumental variable interacts with the endogenous variable. From the first stage regression results, presented in Table 6, the relevance condition of the specific instrumental variables might be inspected, and it can give some insight on the executive compensation contract design. In the case of Vega(ln), it can be observed that previous year performance, measured by one year lagged stock returns variable, Return(t-1), coefficient (β=-468.005) is statistical significant at 5% level and shows a negative impact on Vega(ln). This result supports the theoretical assumption that higher prior period performance, in terms of stock returns, determines compensation committees to induce less risk-taking behavior through lower pay-risk incentives. The current period cash balance to total assets, CashBS, coefficient estimate of 7.854 is significant at 10% level in the Vega equation, and confirm the previous made assumption from Jensen, 1986 and Stulz, 1990, that firms with greater cash balances, US commercial banks in this case, tend to face bigger agency problems, and risk-taking incentives are increased.

Consistent with previously made assumptions based on empirical studies on executive incentives (e.g. Coles et al., 2003; DeYoung et al., 2010; Armstrong and Vashishtha, 2012), the first stage regression indicates a positive and highly significant relationship between CEO tenure and pay-performance incentives (Delta(ln)), (β=0.087). This result supports the assumption that with the time CEO has been in his/her position, he/she becomes more confident in his/her abilities to manage bank's operations and, therefore, becomes less risk-adverse and boards try to control for this factor by inducing greater risk-reducing incentives with high-delta compensation plans. Thus, CEOtenure is a valid instrumental variable for

Delta(ln). As expected, first stage regression coefficient of CashComp(ln), indicates a positive

Table 6

This table displays First stage regression results of the Two Stage Least Squares (2SLS)estimation, endogenous variables (Vega(ln ), Delta(ln) and Total Risk). Prior one year stock returns,Return(t-1), and current year cash balance to total assets, CashBS, - IV for Vega(ln); CEOtenure, and natural logarithm of annual cash compensation , CashComp(ln) IV for Delta(ln) and EconCond - IV for Total Risk. The parameters are estimated based on an unbalanced panel data of 835 annual observations for 83 different U.S. commercial banks, from 2004 to 2014. Robust, cluster on firm level standard errors are reported in brackets. The superscripts ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels.

1.21117*** [0.31851] 0.60597*** [0.04749] -0.00079** [0.00038] 3.64616*** [1.08334] 1.73124*** [0.34688] -0.01023*** [0.00084] -7.63772 [22.27709] 6.06578* [3.51845] -0.18666*** [0.02767] -468.00480** [218.44350] -42.98299 [42.63622] -3.22815*** [0.46941] 7.85407* [5.61719] 1.22991 [0.86935] 0.00824 [0.00860] -0.00730 [0.09553] 0.087115*** [0.01325] -0.00008 [0.00005] 0.40261 [0.58641] 0.35444*** [0.11004] -0.00306*** [0.53784] -0.04195* [0.02465] -0.00236 [0.00395] -0.00007* [0.00003] -8.10998 [5.81818] -5.29213*** [1.01046] 0.07748*** [0.00761] Nr. of observations _{835 835 835} Centered R-squared _{0.1335 0.5181 0.3180} F statistic 7.22 73.83 43.44 p-value (0.0000) (0.0000) (0.0000)

valid, uncorrelated with the error term and correctly excluded from the estimated equations. The p-values of the Hansen J-statistic for each system equation are reported in Table 7, (0.1180; 0.1045 and 0.5085), indicate that the null hypothesis cannot be rejected in all three specified equations, thus, giving confidence that the used instrumental variable sets are appropriate and valid.

Table 7 presents the second stage regression results of 2SLS, from equation (1), (2) and (3) using Total risk as measure of bank risk profile. First column presents the coefficient estimates of the determinants of Total Risk and the corresponding robust cluster standard errors. As it was expected, high-vega compensation incentives are associated with statistically significant, at 0.05 level, increase in daily volatility of stock returns (β=0.00414). This result could be interpreted as high pay-risk incentives influence the CEO in leading the bank activity more towards non-traditional riskier operations, therefore increasing the risk profile, from the viewpoint of investors. Meanwhile, CEO risk-aversion incentives (Delta(ln)) have a negative, but insignificant impact on the daily volatility of the bank stock returns. In their study DeYoung et al. 2010, argue that one explanation for the insignificant effect of Delta, measuring CEO pay-performance incentives on bank total risk, is that this type of incentives induce the CEO to run relatively traditional banking models and undertake projects towards less risky activities with effects quite clear to the investors therefore having little impact on their expectations on stock price change.

Table 7

This table presents the Second stage regression results of the Two Stage Least Squares (2SLS) estimation, for equations (1), (2) and (3) using Total risk as measure of bank risk with endogenous variables: (Vega(ln ), Delta(ln) and Total Risk). Prior one year stock returns,Return(t-1), and current year cash balance to total assets, CashBS, - IV for Vega(ln); CEOtenure, and natural logarithm of annual cash compensation , CashComp(ln) IV for Delta(ln) and EconCond - IV for Total Risk. The parameters are estimated based on an unbalanced panel data of 835 annual observations for 83 different U.S. commercial banks, from 2004 to 2014. Robust, cluster on firm level standard errors are reported in brackets. The superscripts ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels.

Dependent variables Explanatory variables -154.4156 [302.2288] 2.41647 [16.38744] 0.00413** [0.00201] 0.07768 [0.07301] -0.00215 [0.00399] -0.33358 [1.30983] -0.00583* [0.00323] 1.35729** [0.66750] 0.51906*** [0.10824] -0.02318*** [0.00841] 2.75818 [2.59995] 1.47272*** [0.51908] -0.15244 [0.11781] -38.63256 [53.06510] 7.11236* [4.03951] 0.00017* [0.00010] -1039.843 [1075.981] 8.733409 [7.34387] 0.08826*** [0.01452] 0.32649** [0.13462] 0.08621*** [0.02223] -4.50721 [16.1716] -4.70729** [2.32739] Nr. of observations _{835 835 835} Hansen J-statistic 4.274 2.975 0.437 p-value (0.1180) (0.1045) (0.5085)

Crag Donald F-statistic 1.659 2.104 1.456

Stock-Yogo critical value 10% relative bias

Prior period leverage ratio variable, EQratio(t-1), coefficient (β=-0.15244) shows a negative, but insignificant effect on daily stock returns volatility. Consistent with the results of DeYoung et al., 2010, the EconCond variable has a positive statistical significant, at 10% level, effect on bank's total risk profile (β=0.00017). This indicates that banks facing better economic conditions can afford and are more willing to engage in riskier activities than those affected by worse economic conditions.

Regression results for equation (2) and (3) for CEO risk-taking incentives measures, Vega and Delta, are shown in second and third column of Table 7. Regression estimates of equations (2) and (3) show a negative effect of bank risk profile, measured by daily stock volatility, on the level of taking incentives, Vega(ln), and a positive effect on the risk-reducing incentives, Delta(ln), but none of them is significant. Therefore, no conclusion can be drawn concerning the hypothesis that boards, when designing executive compensation packages, take into consideration the expected future bank risk profile from the induced CEO risk-taking behavior. Bank size measured by prior period natural logarithm of total assets,

TAssets(t-1), is positively related to both CEO incentives measures, statistically significant at

5% level in case of Vega(ln), (β=0.418), and at 1% level for Delta(ln), (β=0.418). Natural logarithm of market-to-book ratio is positively associated with both measures of CEO incentives, although statistically significant at 99% confidence level just for Delta equation (β=1.47272). This result is consistent with previous literature indicating that banks with greater investment opportunity sets tend to use stronger executive incentives. Concerning the impact of leverage on executive incentives, it can be observed that only Delta is significantly, at 5% level, affected by EQratio(t-1). The positive coefficient of 7.11236 may indicate that, when designing CEO compensation and establishing the level of risk-taking incentives, boards of banks with stronger capital structure prefer using more equity based executive compensation, therefore inducing stronger incentives.

presence of weak instruments, but this inference might be made when there is only one endogenous variable in the right hand side of the equation. In their paper, Stock, Wright, and Yogo, 2002, designed a diagnostic based on the Cragg and Donald F statistic to test for weak instruments. This test is appropriate when there are more than one endogenous explanatory variables. A Cragg and Donald F statistic much smaller than the critical values proposed by Yogo, 2004, for the case when the bias of the TSLS estimator does not exceed 10% of the bias of the OLS estimator, indicates that some of the used instruments are most probably weak. As it can be noticed in Table7, the equation specific Cragg and Donald F statistics are quite small comparative to the Stock-Yogo critical value 10% relative bias, (1.659<7.56, 2.104<5.78, 1.456<5.78), indicating that the used instruments are only weekly correlated with the endogenous variables, especially for Vega(ln) and Total Risk. One solution for this problem would be to use valid instrumental variables that are more strongly correlated with each of the endogenous instrument, but finding instruments that both the relevance and exclusion conditions hold is hard.

Table 8

This table presents the Second stage regression results of the General Method of Moments Continuous Updating Estimator (GMM-CUE), for equations (1), (2) and (3) using Total risk as measure of bank risk with endogenous variables: (Vega(ln ), Delta(ln) and Total Risk). Prior one year stock returns,Return(t-1), and current year cash balance to total assets, CashBS, - IV for Vega(ln); CEOtenure, and natural logarithm of annual cash compensation , CashComp(ln) IV for Delta(ln) and EconCond - IV for Total Risk. The parameters are estimated based on an unbalanced panel data of 835 annual observations for 83 different U.S. commercial banks, from 2004 to 2014. Robust, cluster on firm level standard errors are reported in brackets. The superscripts ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels.

Dependent variables Explanatory variables -567.9118 [419.6171] 0.50854 [16.22024] 0.00817*** [0.00312] 0.09687 [0.07045] -0.00889 [0.00635] -1.15447 [1.37312] -0.00775 [0.00565] 1.18613 [0.75593] 0.50931*** [0.11205] -0.02342 [0.0149] -0.07299 [3.79537] 1.35061*** [0.49532] 0.02033 [0.19991] -114.3937 [75.45409] 7.66424* [4.05321] 0.00032 [0.00022] -2430.628* [1467.157] 13.75262 [9.736508] 0.08805*** [0.01532] 0.32638** [0.13381] 0.09074** [0.03988] 19.71875 [23.50375] -4.55064** [2.36765] Nr. of observations _{835 835 835} Hansen J-statistic 1.749 2.408 0.430 p-value (0.4172) (0.1207) (0.5122)

Crag Donald F-statistic 1.659 2.104 1.456

Stock-Yogo critical value 10% relative bias

Systematic Risk and CEO incentives

As previously discussed, the regulatory reform, product market innovation, and technological shift had a huge impact on the way US commercial banks operate making them more exposed to the markets they activate in, consequently, increasing their systematic risk. Since the Durbin-Wu-Hausman and Wu-Hausman tests, presented in Table 9, fail to reject the null of exogeneity, I use pooled OLS estimator to investigate the relationship between Systematic risk and CEO risk-taking incentives(Vega(ln) and Delta(ln)).

Table 9

This table displays the results of tests for endogeneity in IV estimation. The null, H0: variables are exogenous, imply that OLS estimator should be used, since it is consistent and fully efficient. Under both tests the null hypothesis is rejected, OLS estimator is inconsistent and estimation methods accounting for endogenous variables should be used.

Tested of endogeneity of , , , Durbin-Wu-Hausma chi-sq (2) test 0.07553 2.55032 0.65993

0.92726 0.11065 0.51716

Wu-Hausman F(2, 825) test 0.15268 2.57017 1.33373

p-value 0.92650 0.1089 0.51332

Table 10

This table presents the pooled OLS estimation parameters for bank risk measured by Systematic Risk. The parameters are estimated based on an unbalanced panel data of 836 annual observations for 83 different U.S. commercial banks, from 2004 to 2014. Robust, cluster on firm level standard errors are reported in brackets. The superscripts ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels.

Dependent variable Explanatory variables 0.00269 [0.00276] -0.04023*** [0.01215] 0.01207 [0.01277] -0.22205*** [0.05326] -2.86321*** [0.99505] -0.00274** [0.00125] 2.17599*** [0.20499] Nr of observations 836 R-squared 0.2474

VI. Conclusion

incentives by employing a simultaneously system of three equations for Risk, Delta and Vega. In the analysis, I employ two variable to represent bank risk profile; daily stock volatility as measure of total risk, most widely used in the literature, and stock market beta, measuring the systematic component of total risk.

Consistent with the predictions, I provide evidence that CEO Vega has a positive significant effect on bank total risk level. This indicates that high pay-risk incentives influence the CEO in leading the bank activity more towards non-traditional riskier operations, therefore increasing the risk profile, from the viewpoint of investors. However, I do not find a significant relationship between systematic component of total risk and risk-inducing incentives, Vega. Equity compensation, through executive stock options (EOS) and restricted stock grants, also induce CEO incentives to decrease the firm's risk profile through his/her equity portfolio sensitivity to stock price change, Delta. I find that Delta has a negative significant impact on bank risk profile, just in the case of systematic risk.

Concerning the effect of risk profile on level of equity incentives, I do not find any significant evidence on the impact of daily stock volatility on risk-taking incentives, Vega, and risk-decreasing incentives, Delta. Therefore no conclusion can be made on the insight that that bank boards are influenced by firm risk expectations when designing CEO compensation packages.

From an empirical perspective, this analysis bring evidence on the relationship between risk-taking incentives and risk profile of banking institutions by approaching a more restrictive setting that what was employed in other studies investigating this line of corporate governance; using instrumental variables estimation methods to control for the endogenous variables issue. Nevertheless, the results demand further research on other factors influencing executive compensation design and executive incentives. Identifying and employing estimations using stronger valid instrumental variables is critical in coming with a less biased estimation of the relationship between executive risk-taking incentives and bank performance.

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Appendix

Table A.1 Average compensation characteristics US commercial banks CEO for period 2004-2014, decomposed by year Year Nr. Obs. Equity Compensation (%) Cash Compensation (%) Other Compensation (%) Delta ($ ths) Vega ($ ths) 2004 52 47.95078 49.30898 2.74024 651.2025 301.195 2005 51 40.54211 53.5449 5.91298 584.4053 358.7588 2006 70 60.53341 39.46659 0 637.8372 171.121 2007 83 54.00257 45.99743 0 425.8269 140.5085 2008 83 48.62499 51.37501 0 261.7744 97.54698 2009 83 42.91855 57.08145 0 244.2549 87.64319 2010 83 46.63831 53.36169 0 289.7469 111.7044 2011 83 54.3038 45.6962 0 239.3914 98.81041 2012 83 59.27696 40.72304 0 283.1193 106.7864 2013 83 64.52662 35.47338 0 404.2364 93.20965 2014 83 62.98161 37.01839 0 483.3583 83.09026

Fig. A.1 Vega and Delta evolution

0.0000 100.0000 200.0000 300.0000 400.0000 500.0000 600.0000 700.0000 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Mean risk-taking incentives

Fig. A.3 Weak instrumental variables confidence region for Total Risk 2SLS estimation equation

Fig. A.4 Weak instrumental variables confidence region for Vega(ln) 2SLS estimation equation -. 0 2 -. 0 1 0 .0 1 .0 2 b e ta : ln _ d e lt a -.005 0 .005 .01 .015 beta: ln_vega 95% Confidence set beta: ln_vega -0.00 beta: ln_delta 0.00 R e je c ti o n p ro b . = 1 -p v a l 0.01 -0.02 -0.00 0.01 0 .25 .5 .75 1 Rejection surface

Anderson-Rubin Confidence Region

-5 0 5 b e ta : ln _ d e lt a -1500 -1000 -500 0 500 1000

beta: Daily Vol 95% Confidence set

Fig. A.5 Weak instrumental variables confidence region for Delta(ln) 2SLS estimation equation -5 0 0 50 1 0 0 b e ta : D a ily V o l -.2 0 .2 .4 beta: ln_vega 95% Confidence set beta: ln_vega -0.21

beta: Daily Vol