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How has the financial crisis affected the relation between incentive
based compensation and bank risk?: Evidence from US banks
MSc Finance
Willem Hasenaar, 1879952 MSc Finance
Supervisor Drs. B. van Oostveen January 2016
Words: 11,603 Abstract
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1. Introduction
Many argue that the structure of executive compensation has played an important role in encouraging bank managers to induce in excessive risk taking that led to the financial crisis. (Acharya et al., 2009; Diamond and Rajan, 2009; Jian, Cherny and Milbourn, 2010; Stiglitz, 2010). In order to find whether incentive based pay packages contribute to higher risk this paper aims to find if ex ante incentives in CEO compensations are associated with ex post risk taking in US banks from 2006-2014.
The use of incentive based pay in compensation package can lead to managers being too eager in maximizing their own value which might induce them to take on excessive risk for the firm. Shareholders (principal) often develop an environment in which an executive’s (agents) interests do not align with their own. This is referred to as the principal-agent problem (Holmstrom, 1979). A method often used by shareholders to overcome this principal agent problem is to incentive managers by providing them with insider ownership in the form of stocks and stock options. This reduces agency cost (Belghitar, and Clark, 2015) and incentivizes managers to aim for growth opportunities and focusing on enhancing firm value by making their pay dependent on the return and the volatility of the underlying stock.
Several previous researches have analyzed the effect of incentive based pay packages on bank risk (Bai and Elyasiani, 2013; Belkhir & Chazi, 2010; Chen, Steiner and Whyte, 2006; DeYoung, Peng and Yan, 2013; Yang, 2010). However, these previous researches focus on the early 2000s and on the period leading up to and during the 2007-2009 financial crisis. During the financial crisis bank CEOs suffered large declines in their stock-based wealth (Fahlenbrach and Stulz, 2011), which may have materially altered their sensitivities to risk and return.
Recent changes in legislation and the following regulatory changes make further investigation of the relation between incentive based compensation and managerial risk-taking imperative. Since the start of the 1980s1 the US financial sector has witnessed a constant flow of deregulating reforms which broadened bank’s their investment opportunities. To encourage managers to exploit these new investment opportunities bank boards increased managerial wealth sensitivities through the use of stocks and stock options (Hubbard and Palia, 1995; Chen, Steiner and
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3 Whyte, 2006). Following a long period of deregulating reforms the US financial sector is currently undergoing a period of increasing regulation following the implementation of the Dodd Frank act in 2010. This act was signed into federal law on 21st July 2010 as a response to the deficiencies shown in regulation by the financial crisis. The Dodd Frank act entails major financial institutional reforms with the intent of cleaning up the consequences of the past decade's financial sector decline by focusing on stability and focusing on investor and consumer protection.
I am among the first to first to examine the effect of incentive based compensation on bank risk-taking in the aftermath of the financial crisis. In this research I will examine the effect of both a CEO´s wealth sensitivity to risk(vega) and a CEO´s wealth sensitivity to performance (delta) on bank risk. Vega, or pay-risk sensitivity, captures the change in the dollar value of CEO wealth for a 0.01-unit change in stock return volatility. Delta is measured as the change in CEO wealth for a 1% change in stock price. Has the increasing regulation that is accompanied with implementation of the Dodd Frank Act influenced the relation between these wealth incentive and risk-taking by bank CEO’s? In order to attempt to answer this question I will compare the effect of vega and delta on bank risk before and after the implementation of this legislative reform. It is important to see how such an increasing regulated environment in which risk-taking is limited may have influenced the effect of incentive based pay on CEO risk-taking. This will give insights into how this regulation influences the effectiveness by which bank boards can control CEO risk-taking through the use of incentive based compensation.
4 The remainder of this research is organized as follows. Section 2 presents the literature review in which the hypotheses are developed. Section 3 contains a description of the data and methodology. Section 4 presents the empirical results. Section 5 presents the conclusion and finally section 6 contains a discussion.
2. Literature review
Since convexity in an incentive scheme generates a positive relation between a manager's wealth and firm risk, compensation components with convex payoffs, such as stock options and common stock, can induce risk-averse managers to invest in valuable risk-increasing projects that they may otherwise forgo (Guay, 1999). Core and Guay (1999) show that firms use annual grants of options and restricted stock to CEO’s to manage their optimal level of equity incentives. By making the CEO’s wealth sensitive to stock risk through the use of options in compensation packages CEO’s are rewarded for increasing stock return volatility. In this light Bebchuck and Spamann( 2010) argue that equity based compensation can indeed to lead to higher risk-taking. Because bank executives expect to share in any gains that might flow to common shareholders, but are insulated from losses that the realization of risks could impose on preferred shareholders, bondholders, depositors, and taxpayers, executives have incentives to give insufficient weight to the downside of risky strategies.
Previous researches on incentive based -pay and risk-taking within banks provide evidence that a higher vega encourages CEO’s to induce in higher risk-taking. In their research Chen, Steiner and Whyte (2006) find that the structure of executive compensation (proxied by stock options as a percentage of total compensation) induces risk-taking in the banking industry over their sample period from 1992-2000. Related to this Bai and Elyasiani (2013) investigate the relationship between insolvency risk and executive compensation for US Bank Holding companies (BHCs) from 1992–2008. They find that higher vega induces the CEOs to implement riskier policies, such as increasing non-traditional banking activities, leading to higher return volatility and lower bank stability. These findings are supported by DeYoung, Peng and Yan (2013) who find that on average during their 1995–2006 sample period, US banks in which CEOs had high pay-risk sensitivity (high-vega banks) exhibited substantially larger amounts of both systematic and idiosyncratic risk. Moreover do Belkhir & Chazi (2010) and Yang(2010) find that vega is positively related bank risk.
First of all I will research how the level of vega will influence the level of bank risk over the full sample period 2006-2014. Based on the findings of previous researches in the banking industry this leads me to the following hypothesis:
5 The implications of delta on managerial risk-taking are theoretically and empirically ambiguous. According to Benson, Park and Davidson (2014) the effect of high delta on stock return volatility depends on whether the increase in value of the manager’s portfolio of stock and options, due to higher risk, outweighs the decrease in value in the manager’s expected utility resulting from increased volatility. Implying that a higher delta might have increased risk-taking incentives as well as decreasing risk-taking incentives and that this depends on a CEO´s expected utility for taking risk. To motivate an effort-averse as well as risk-averse manager (the agent) to exert optimal effort, compensation should be tied to performance(Dai, Jin and Zhang, 2014). Increased pay for performance sensitivity can mean that managers will work harder or more effectively because managers share gains and losses with shareholders. The sensitivity of a CEO’s wealth to stock price, or delta, is therefore seen as aligning the incentives of managers with the interests of shareholders. Besides aligning interest with shareholders increased delta also exposes managers to more risk. This is because managers with higher delta are undiversified with respect to firm-specific risk and are therefore exposed to more risk than diversified shareholders (Holmstrom, 1979). Hence the principal agent model predicts that higher deltas could exacerbate managerial risk aversion (Amihud and Lev, 1981 and Smith and Stulz, 1985). In support of this prediction Deyoung, Pen and Yan (2013) finds that CEO delta is negatively related to risk taking in banks. On the other hand can it also be expected that a high delta increases managerial risk-taking. High delta might increase a CEO´s effort to identify and commit to risky and positive NPV projects as this possibly maximizes his own wealth. In light of this theory Belkhir & Chazi( 2010) find that an increased pay-for performance sensitivity is related to an increase in bank risk. Considering these contradictory findings I present competing hypotheses regarding the effect of delta on bank risk:
H2A: Banks in which CEO’s receive a higher delta will exhibit lower risk, ceteris paribus, than banks in which CEO’s receive a lower delta.
H2B: Banks in which CEO’s receive a higher delta will exhibit higher risk, ceteris paribus, than banks in which CEO’s receive a lower delta.
Because I set up two contradicting hypothesis the overall effect of delta on risk-taking will become an empirical question.
The effect of Regulation
6 The Dodd Frank Act might have major implications for banks as it limits them to perform and invest in profitable but risky projects and might therefore induce them to take on less risky business policies. Resulting in bank boards to be more precarious to incentivize their executives with risk sensitive pay packages. The Dodd–Frank Wall Street Reform and Consumer Protection Act (commonly referred to as Dodd-Frank2) was signed into federal law by President Barack Obama on July 21, 2010 as a response to the deficiencies shown in regulation by the financial crisis. The Dodd Frank Act runs approximately 2,300 pages, addressing a broad range of issues concerning financial institution reform within its 16 titles including systemic risk, disposition of insolvent financial institutions, insurance industry monitoring, proprietary trading in banks, derivatives (swaps in particular), investor and consumer protections.
Deregulation in the banking industry preceding the financial crisis is perceived to have led to an increase in the vega effect on bank risk (Chen, Steiner and Whyte, 2006; Belkhir & Chazi, 2010; DeYoung, Peng and Yan, 2013). It is often being described as one of the main determinants of the excessive risk taking in the financial industry that eventually led to the financial crisis (Adelson, 2013.; Sabato, 2010). According to Crawford, Ezzell, and Miles (1995) and Hubbard and Palia (1995) deregulation creates a more competitive environment, and results in an expansion of managerial discretion and the banking industry’s investment opportunity set. To encourage CEO’s to exploit the new investment opportunities available through deregulation bank boards increased CEO’s wealth sensitivity to risk (Belkhir & Chazi, 2010). In their paper Belkhir & Chazi (2010) look at the effect deregulation has on the level of CEO vega within banks. Besides identifying factors that determine the level of vega they look at how the level of vega differs between the period pre-deregulation and the period post deregulation. Thereby defining the period 1993-2000 as the period of pre-deregulation and the period 2000-2005 as the period of post-pre-deregulation because of the passage of the Gramm-Leach Bilely act in 19993. They find a positive relation between vega and deregulation meaning that vega increased post deregulation in the US banking industry. Following these results DeYoung, Peng and Yan (2013) find that that CEO’s responded systematically to the increasing vega as the effect vega increased significantly upon the early 2000s industry deregulation.
As opposed to the positive effect of deregulation on vega, as found in previous researches I
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The act's numerous provisions, spelled out over thousands of pages, are scheduled to be implemented over a period of several years and are intended to decrease various risks in the U.S. financial system The act
established a number of new government agencies tasked with overseeing various components of the act
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7 expect that increased regulation following the Dodd Frank act will negatively influence the effect of vega in the banking industry. The renewed regulation limits banks to invest in risky products (such as derivatives) and requires them to focus on long-term stability. These factors limit the risk-taking possibilities of banks and hence might affect the business policies and strategies pursued by banks. Caluzzo and Dong (2015) find that financial institutions on an individual basis did in fact reduce their risk exposures post crisis compared to pre-2007-2009 crisis levels. Indicating that banks are shifting their business policies towards a lower level of risk taking and focusing on increasing their overall stability. This shift of focus and change in business policies reduces the overall risk-taking and might in turn mitigate the effect CEO vega has on the risk taken by a CEO. To reduce the level of risk-taking and shift the focus towards long-term stability and performance bank boards might adjust the risk incentive based pay to its managers accordingly.
Increased disclosure requirements and focus on investor protection associated with the increased regulation might, besides reducing investment opportunities, also negatively influence the vega effect on risk in the banking industry. In their paper Chen et al (2015) examine the relation between the sensitivity of CEO’s compensation portfolio to stock return volatility (vega) and audit fees and find that a higher CEO vega leads to higher audit prices. Building on the same idea as Coles, Daniel, and Naveen (2006) who suggest that a higher CEO vega is likely to induce managers to increase risk-taking, higher wealth sensitivity to risk will, consequently, result in a CEO to engage more in financial misreporting. These risk incentives are known by audit firms which leads them to incorporate these incentives in their assessment of litigation risk when setting audit prices, eventually leading to higher audit fees. Meaning the level of audit fees can be considered as a level of risk as perceived by audit firms and that a higher vega increases this risk. Chen et al (2015) also look at how a change in accounting regulation, the Sarbanes-Oxley Act (SOX)4, influences the effect of vega on audit fees. They find that the positive association between vega and audit fees is weaker in the post-Sarbanes-Oxley Act (SOX) period. In a sense the SOX has similar implications as the DODD Frank. Both focus on increasing corporate disclosure and aim at restoring confidence of investors. This reduced effect of vega on audit fees (risk) because of increased disclosure regulation might therefore also apply to the effect of vega on bank risk with the implementation of the Dodd Frank Act.
Following the above this leads me to the following hypotheses with regards to vega and its effect on bank risk in the period post implementation of the Dodd Frank Act:
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H3: The effect vega has on bank risk has decreased post implementation of the Dodd Frank
Act.
Because the implications of delta on managerial risk-taking are theoretically and empirically ambiguous I do not expect a difference in effect before and after the implementation of the Dodd Frank Act. In their paper Crawford, Ezzell, and Miles (1995) show that pay-performance sensitivities increased during the deregulation in the 1980s for bank CEOs. They argue that bank boards increased delta to encourage bank managers to exploit new investment opportunities made possible by the gradual elimination of state-level barriers to geographic expansion. Contrary it might be expected that an increasing regulation with reducing investment opportunities will lead to bank boards to reduce delta. This in turn might reduce the effect delta has on bank CEO risk-taking. However, as previously stated, do both theory and empirical findings suggest that there is no explicit effect of delta on managerial risk-taking. Because of reduced investment opportunities and increased capital requirements with the implementation of the Dodd Frank act banks are forced to reduce risk exposures compared to pre regulation levels. As increased CEO delta might also reduce risk-taking by the CEO as opposed to increased taking, bank boards might incentivize the CEO to reduce risk-taking and pursue less risky policies by increasing delta. Hence likely increasing the effect delta has on bank risk. As these arguments above might offset each other I arrive at the following hypothesis with regards to delta and it effect on bank risk post-regulation:
H4: The effect delta has on bank risk has not changed post implementation of the Dodd Frank Act.
3. Data and Methodology
1. Required data.To perform this research I collect data regarding executive compensation from Standard & Poors Execucomp database. This database provides data on all components of executive compensation (salary, bonus, stock and option holdings) and covers the S&P 1500 plus companies, as well as the companies removed from the S&P1500 index but still trading. Execucomp collects compensation data on up to nine executives, though most companies report only five executives. Execucomp identifies executives as CEOs and documents the dates. Similar to Fahlenbrach and Stulz (2011) I use SIC codes 6000-63005 to obtain compensation data for all bank types. From the Federal Reserve’s consolidated financial statements for bank holding companies (Y-9C reports) I obtain balance sheet and income data. The Y-9c reports collect quarterly financial data for banks on a consolidated basis in
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These include depository institutions, non-depository Credit Institutions and Security and commodity brokers, dealers, exchanges, and services. Insurance companies, real estate companies and holding and other
9 the form of balance sheet, income statement and detailed reporting schedules. In order to create a consistent data series with compensation data, I retain the fourth quarter data from the Y-9C reports. Finally I obtain data on stock returns from the Center for Research in Security Prices (CRSP) database. In order to perform the analysis I will intersect the available data on banks in Execucomp, the Y-9c reports and the CRSP database.
I start with a sample of 441 banks (3061 observations) from Execucomp and finally arrive at a sample of 105 banks with 681 bank-year observations through the process of merging the databases.
2. Analysis
The period I will be analyzing runs from 2006 to 2014. Thereby capturing the effect of risk sensitive pay in the financial crisis of 2007-2009 and the period post financial crisis in which regulation increases. To measure the level of risk taken by a CEO I will use three market based risk measures. Guégan and Tarrant (2012) show the need for the information from multiple risk measures in order to determine a bank's loss distribution.
In estimating the effect of vega and delta on bank risk I will use the following equation: Riski,t= β0+ β1 × lnVegai,t−1+ β2 × lnDeltai,t−1+ β3× lnTotal Assetsi,t−1+ β4×
MTB Ratio i,t−1+ β5 × Equity Ratioi,t−1+ c𝑖+ μt+ εi,t (1)
where i is an index for the bank and t is a time index, Risk is a proxy for bank risk, β0is a constant, β1 a coefficient vector for vega, β2 a coefficient vector for delta, β3, β4 and β5 are coefficient vectors for
the control variables: total assets, market to book ratio and equity ratio, c𝑖 is a firm-fixed effect, μt is
a time-fixed effect and εi,t is the error term. Because the distributions of vega, delta and total assets
are heavily skewed to the right, I specify them in natural logs. Three versions of this equations are
estimated where Riski,t is proxied by total risk (model 1), systematic risk (model2) and idiosyncratic
risk (model 3)).
I use lagged variables of vega and delta which allows for the risk incentives established in year t-1 to effect the risk taking by the CEO in year t. It is possible that the CEO wealth incentives (vega and delta), which are right-side variables, are affected by the level of risk, the left hand-side variable, and hence the model is subject to endogeneity problems. Using lagged variables I mitigate the possible effect of reverse causality between the left hand side variable risk and the right hand side variables vega and delta.
10 both the effect of vega on risk and the effect of delta on risk. In estimating the change in effect of vega on bank risk after the increasing regulation I will use the following modified version of equation (1):
Riski,t= β0+ β1 × lnVegai,t−1+ β2 × lnDeltai,t−1+ β3× lnTotal Assetsi,t−1+ β4×
MTB Ratio i,t−1+ β5 × Equity Ratioi,t−1+ β5 × Regulationi,t+ β6 × Vega ∗ Regulationi,t−1+
μt+ εi,t (2)
In estimating the change in effect of delta on bank risk after the increasing regulation I will use the following modified version of equation (1):
Riski,t= β0+ β1 × lnVegai,t−1+ β2 × lnDeltai,t−1+ β3× lnTotal Assetsi,t−1+ β4×
MTB Ratio i,t−1+ β5 × Equity Ratioi,t−1+ β5 × Regulationi,t+ β6 × Delta ∗ Regulationi,t−1+
μt+ εi,t (3)
The regulation variable in equation (2) and (3) is a dummy variable that takes on a value of 0 for the years prior to 2011 and a value of 1 for the year 2011 and onwards. Although the Dodd Frank Act has been implemented in 2010 the first year in my sample in which regulation can influence the effect of incentive based compensation will be 2011 because I use lagged variables for vega and delta.
Risk Measures
To measure bank risk I will use three types of market based risk measures. The market based risk measures that I will be using are total risk, systematic risk and idiosyncratic risk. Total risk is calculated as the daily average standard deviation of a bank’s stock return (σj). Systematic risk and idiosyncratic risk are obtained from the CAPM regression as show in equation (4) below:
𝑅𝑗 − 𝑅𝑓 = 𝛼 + 𝛽𝑚𝑗 (𝑅𝑚− 𝑅𝑓) + 𝜇𝑗 (4)
11 Wealth sensitivity measures
The CEO’s wealth sensitivities I will be measuring are the CEO’s wealth sensitivity to risk (vega) and the CEO’s wealth sensitivity to performance (delta). For the wealth sensitivity to risk I use vega of the CEO’s option portfolio because the aggregate sensitivity of CEOs’ stock-based wealth to risk is driven primarily by stock options (Guay, 1999).
Vega
Vega, or pay-risk sensitivity, is estimated as the partial derivative of the option value with regards to stock return volatility multiplied by 0.01 and the total number of options. It captures the change in the dollar value of CEO wealth for a 0.01-unit change in stock return volatility. Vega can vary widely based on a bank’s financial characteristic, total of number of options held by the CEO and the specific parameters underlying the valuation of stock options, such as the exercise price and the time to maturity of the option. The total vega of a CEO’s option portfolio is calculated as the sum of the individual option vega’s.
Delta
Delta or pay-performance sensitivity, is the total of delta of options holdings and delta of stockholdings. Option delta is estimated as the partial derivative of the option value with regards to stock return volatility multiplied by 1%. The delta of stocks is simply estimated by multiplying the number of shares with 1% of the current stock price.
Calculating vega and delta
Similar to Guay (1999) I estimate the incentive effects of employee stock options using the Black Scholes formula for valuing European call options, as modified to account for dividend payouts by Merton (1973). A more detailed description on the calculation of the option values, vega and delta can be found in appendix I. Following Core and Guay (2002) I estimate the missing parameters for calculating option values, vega and delta using the one year approximation (OA) method. Core and Guay (2002) show the validity and robustness of their approximation.
12 Control variables
In this research I will control for bank size, bank investment opportunities and bank leverage.
Bank size
Bank size is measured by the natural logarithm of total assets. One of the main factors perceived causing distortion in financial firm’s risk-taking incentives has been the TBTF (too big to fail) policy of the government (Boyda, Jagannathan, and Kwak, 2009). When firms are perceived to be too big to fail (TBTF), they have a propensity to assume excessive risks to profit in the short term as they have limited downside risk. Using a sample of US financial institutions between 2002-2012 Bhagat, Bolton and Lu (2015) find that bank size is positively related to risk-taking. It is therefore important to look how a bank’s size influences the level of risk taking by executives.
Investment opportunities
Investment opportunities are measured by market to book ratio. In their research Belkhir & Chazi (2010) find that larger BHCs with better investment opportunities reward their CEOs with a compensation that has a higher sensitivity to risk. It is therefore important to look how a bank’s investment opportunities influence the level of risk taking by executives.
Leverage
13 3. Descriptives
Table 1 reports the annual statistics for banks in the sample for the period 2006-2014. To reduce
the influence of extreme values, I winsorized all variables at the 1st and 99th percentiles of their
sample distributions.
Panel A reports the bank risk and asset data. The average asset size of the banks in my sample is $ 134bln. The asset size is highly skewed to the right as the banks in the top quartile are more than 4 times bigger than the median size banks. I therefore use the natural logarithm of total assets as a proxy for firm size to reduce the effect of skewness in my results. The average daily standard deviation of stock returns is 2.64% over the sample period. This is considerably larger than
the standard deviation of bank stock returns as found in previous studies. Deyoung, Pen and Yan
(2013) find an average daily standard deviation of 1.70% from 1995-2006 and Bai and Elyasiani (2013) find an average standard deviation of 1.86% from 1992-2008. The most plausible reason for this substantially higher standard deviation of stock returns is that my sample fully captures the volatile period of the financial crisis. Average daily standard deviation of stock returns of the banks in my sample heavily increases for the years 2008-2010 to eventually return to pre-crisis levels in 2012, as can be seen from figure(1). The average systematic risk, measured as the beta of the CAPM, is 1.34 over the sample period. Idiosyncratic risk, measured as the standard deviation of the residuals of the CAPM averages at 1.96% over the sample period.
Figure 1: Total risk, measured as the daily average standard deviations of stock returns of all the banks in the sample (681 observations) from 2006-2014.
14 Table 1: Descriptive statistics for US banks and their CEO’s over the 2006-2014 period.
Variable N Mean Median STD Min P25 P75 Max
Panel A:
Stock return standard deviation % 681 2.64 1.97 1.75 0.84 1.41 3.17 9.41 Systematic risk (Beta) 681 1.34 1.28 0.40 0.65 1.07 1.52 2.85 Idiosyncratic Risk % 681 1.96 1.43 1.43 0.66 1.08 2.29 8.08 Total Assets $ bln 681 134.00 11.70 396.00 0.59 5.15 45.30 2,180.00 ln Total Assets 681 16.67 16.27 1.79 13.28 15.45 17.63 21.50 Equity Ratio % 681 10.77 10.47 3.26 4.45 8.80 12.09 28.32 Market to book ratio 680 1.32 1.21 0.67 0.12 0.89 1.63 3.73
15 Panel B of table 1 reports the summary statistics of the bank CEO’s compensation and associated wealth sensitivities. In a given year the mean (median) total compensation of a CEO is $4,608,590 ($2,364,670) with a standard deviation of $5,247,890. The mean (median) CEO vega is $167,320 ($31,560), suggesting that for a 1% increase in stock return volatility CEO option holdings value increases by $167,320 on average. The mean (median) CEO delta for banks is $466,560 ($116,750) suggesting that for a 1% increase in stock price the combined value of a CEO’s option holdings and
stock holdings increases by $466,5606. Because the distributions of these estimated variables are
heavily skewed to the right, I specify them in natural logs. Figure (2) displays the development of vega and figure (3) the development of delta over the sample period. These figures show that vega and delta decreased heavily during the financial crisis in 2007 and 2008. One plausible explanation for this sharp decline of vega and delta could be the reduction in the use of options and stocks in the CEO compensation contracts. Between 2006 and 2008 the average number of CEO option holdings dropped by 28.75% (1- 885,337/1,242,665) whereas the average number of CEO stock holdings dropped by 20.53% (1-1,338,850/1,684,754). A figural display of the total option and stock holdings can be found in appendix III.
Figure 2: The dollar value of vega (the dollar change in the CEO’s wealth for a 0.01 unit change in standard deviation of stock returns) for CEO in banks (681 observations) from 2006-2014.
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In comparison I find substantial higher values of CEO vega and delta for industrial firms over 2006-2014. Over a sample of 176 industrials (1310 observations) I find a mean (median) vega of $ 277,594 ($ 134,625) and a mean (median) delta of $ 662,511 ($ 335,036). These results indicate that CEO’s of banks have lower compensation sensitivities to stock return volatilities and stock price sensitivities as those in industrial firms. Therefore, the incentive feature of management compensation is different for banks and industrial firms. This finding is supported by Houston and James (1995) who find that bank CEOs indeed receive a smaller percentage of their compensation in the form of options and stocks, than CEOs in other industries.
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Figure 3: The dollar value of delta (the dollar change in the CEO’s wealth for a 1% change in stock price) for CEO in banks (681 observations) from 2006-2014.
A detailed correlation matrix can be found in appendix II. Since all correlations are below 0.8 multicollinearity does not seem to be an issue in my model.
4. Results
This section presents the results of this study and consists of two parts. In the first part, the baseline, I present the results from the OLS estimations in order to determine the effect of vega and delta on bank risk. In the second part, the regulation effect, I will look at the difference in effect of vega and delta on bank risk before and after the implementation of the Dodd Frank Act.
Baseline
Table 2 shows the results of the OLS estimation, where risk is regressed on the natural log of vega, delta and the control variables. In columns 1,2 and 3 risk is measured by three types of market based risk measures: (1) total risk, (2) systematic risk and (3) idiosyncratic risk. This structure holds throughout the paper. In these OLS estimations the standard errors are corrected for group correlation within banks and heteroscedasticity7.
Column 2 shows that the level of vega positively affects systematic risk at the 1% significance level which is in line with my previously stated vega hypothesis that a higher vega leads to higher risk.
7The results from the modified Wald-test show that there is a groupwise heteroscedasticity in
the fixed effects regressions. For all risk measures the null hypothesis, that the residuals are homoscedastic, is rejected at the 1% level.
17 Table 2: This table shows the results of OLS estimations without inclusion of firm-fixed and time-fixed effects using a US sample of 105 banks over the 2006-2014 period. Since I work with a 1-year lag, the dependent variables used are for the 2007-2014 period, and the independent variables are for the 2006–2013 period. Model 1 report results when the risk is measured by total risk; Model 2 report results when the risk is measured by systematic risk and Model 3 report results when the risk is measured by idiosyncratic risk. lnVega is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock return volatility. lnDelta is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock price. lnAssets is the natural log of total bank assets; Market to book is the bank’s market-to-book ratio of equity; Equity ratio is total equity capital over total assets. ***, **, * Represent significance at the 1%, 5% and 10% levels respectively. The robust standard errors are shown in parentheses under the coefficients.
(1) (2) (3)
Total risk Systematic risk Idiosyncratic risk
Constant 0.0463*** 0.974*** 0.0440***
(0.0104) (0.239) (0.00828)
lnVegai,t-1 -6.88e-05 0.0471*** -0.000586
(0.000741) (0.0171) (0.000598)
lnDelta i,t-1 -0.00209** -0.0552*** -0.00169***
(0.000824) (0.0190) (0.000650)
LnAssets i,t-1 0.000445 0.0359** 0.000137
(0.000646) (0.0145) (0.000512)
Market to book i,t-1 -0.00339*** -0.0812*** -0.00358***
(0.00128) (0.0303) (0.00101)
Equity ratio i,t-1 -0.105*** -0.301 -0.103***
(0.0315) (0.676) (0.0258)
Observations 506 506 506
R-squared 0.095 0.091 0.150
No statistical significant coefficients are found for vega when risk is measured by total risk or idiosyncratic risk. With regards to the pay-performance sensitivity I find that the level of delta negatively affects risk for all three risk measures (columns 1,2 and 3).The significance of these coefficients however differ over the three risk measures. This negative effect is significant at the 5% level for total risk and significant at the 1% level for systematic risk and idiosyncratic risk.
With regards to the control variables I find that bank size, measured by total assets, positively effects risk when measured by systematic risk and is statistically significant at the 5% level. There is no significant effect of bank size on total risk and idiosyncratic risk. Columns 1,2 and 3 show that a higher market to book ratio negatively effects risk within banks over all three risk measures at the 1% significance level. The same holds for the effect of leverage on total risk and idiosyncratic risk. The effect of leverage on systematic risk is not statistically significant.
As omitted variables possibly bias results from OLS estimations, these need to be accounted for with firm-fixed and time-fixed effects. Hence, Table 3 shows results of OLS estimations where firm-fixed and time-fixed effects are included8.
8 The results from the Hausman test for random correlated effects show that only the estimates of the fixed
18 Column 2 shows that the positive effect of vega on systematic risk remains statistically significant with the inclusion of firm and time fixed effects, however now at the 5 % significance level. The coefficient has slightly increased from .000471 to .000476 compared to the regression without the inclusion of these fixed effects. In addition to systematic risk columns 1 and 3 now show a positive significant effect of vega on total risk and idiosyncratic risk at the 5% significance level with the inclusion of firm and time fixed effects. In contrast to changes in effect for vega I find similar results for delta on risk when including firm and time fixed effects. From column 1, 2 and 3 it can be seen that delta negatively influences risk at the 1% significance level for all three risk measures.
The results in this section show that vega and delta have opposite effects on bank risk. With increased CEO’s personal wealth sensitivity to stock return volatility the CEO will have a stronger incentives to take risk thereby increasing the overall bank risk. However as the performance sensitive pay increases, the CEO, now facing a potentially greater loss from risk-taking, will become more risk averse and will implement safer investment policies, leading to lower overall bank risk. With the latter providing a somewhat stronger incentive for a CEO to reduce risk than the risk sensitive pay does to increase risk. These negative significant coefficients for delta indicate that the negative delta hypothesis(2) dominates the positive delta hypothesis (2a).
This somewhat contradicts previous studies who find a stronger positive effect of vega on risk than they do for the negative effect of delta (Coles, Daniel, and Naveen 2006; Belkhir and Chazi, 2010; Deyoung, Pen and Yan, 2013). A possible explanation for this result might be related to the reduction in the level of vega over the sample period as can be seen from figure 2. To sufficiently reduce a CEO’s risk aversion and hence induce him/her to take on higher risk might require a minimum level of risk sensitive pay. It might be so that the level of vega has been approaching this minimum requirement over the sample period thereby reducing the effect of a CEO’s vega on his/her risk-taking. As CEO’s are generally perceived to be risk averse this reduction in vega might have triggered the incentive provided by delta to induce in lower risk-taking.
19 Table 3: This table shows the results of OLS estimations with inclusion of firm-fixed and time-fixed effects using a US sample of 105 banks over the 2006-2014 period. Since I work with a 1-year lag, the dependent variables used are for the 2007-2014 period, and the independent variables are for the 2006–2013 period. Model 1 report results when the risk is measured by total risk; Model 2 report results when the risk is measured by systematic risk and Model 3 report results when the risk is measured by idiosyncratic risk. lnVega is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock return volatility. lnDelta is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock price. lnAssets is the natural log of total bank assets; Market to book is the bank’s market-to-book ratio of equity; Equity Ratio is total equity capital over total assets. With respect to all estimations Hausman tests are performed to determine whether a firm-fixed effect is preferred over a random effect. All Hausman tests yield significant results and reject the null hypothesis that the difference in the coefficients is not systematic at a 1% level. Hence, only the coefficients of firm-fixed effect estimations are consistent. ***, **, * Represent significance at the 1%,5% and 10% levels respectively. Robust standard errors are shown in parentheses under the coefficients.
(1) (2) (3)
Total risk Systematic risk Idiosyncratic risk
Constant -0.0366 -0.659 -0.0253 (0.0408) (1.615) (0.0374) lnVegai,t-1 0.00112** 0.0476** 0.00106** (0.000552) (0.0238) (0.000486) lnDelta i,t-1 -0.00288*** -0.115*** -0.00279*** (0.00106) (0.0281) (0.000938) LnAssets i,t-1 0.00589** 0.162* 0.00500** (0.00239) (0.0961) (0.00220)
Market to Book i,t-1 -0.00732*** -0.0981* -0.00749***
(0.00190) (0.0546) (0.00158)
Equity ratio i,t-1 -0.138*** -0.149 -0.157***
20 To examine whether the level of vega influences the risk incentive of CEO’s I will compare CEO’s in banks who receive a relatively high vega (high vega CEO’s) to CEO’s in banks who receive a relatively low vega(low vega CEO’s). CEOs with higher cash compensation are more likely to be entrenched and tend to become more risk averse (Berger et al , 1997). I will therefore determine whether a CEO is a high vega CEO or a low vega CEO by the ratio of vega/total current compensation to eliminate differences in risk aversion between CEO’s. Total current compensation consists of the salary + cash bonus and thereby compromises the total cash compensation as received by the CEO.
High vega CEO´s are those observations which are in the top 50% of the vega/total current compensation ratio. Low vega CEO´s are those observations which are in the bottom 50% of vega/total current compensation ratio. I use the one year lagged value of the vega/total current compensation ratio as vega is also lagged by one year in the regression model. Table 4 presents the results of the high vega CEO (Panel A) vs low vega CEO (Panel B). Columns 1,2 and 3 show that the vega coefficients only show statistical significance for the subsample of high vega CEO’s. The positive vega coefficients for high vega CEO´s are statistically significant at the 1% level for total risk, and at the 5% level for systematic risk and idiosyncratic risk. Indicating that the significant positive effects of vega on total risk, systematic risk and idiosyncratic risk as found in table 3 are primarily driven by high vega CEO´s. Additionally columns 1,2 and 3 of Panel A show similar statistical significant results for delta on the three risk measures as in the full sample results of table 3.
21 Table 4: This table shows the results of OLS estimations with inclusion of firm-fixed and time-fixed effects of the high vega and low vega observations for the 2006-2014 period. The results of the subsample of high vega observations are presented in Panel A and the results of the subsample of low vega observations are presented in Panel B. Ranking of high and low vega observations is determined by the ratio of vega to total current compensation. High vega observations are those observations which are in the highest 50% of the ratio. Low vega observations are those observations which are in the lowest 50% of the ratio. Since I work with a 1-year lag, the dependent variables used are for the 2007-2014 period, and the independent variables are for the 2006–2013 period. Model 1 report results when the risk is measured by total risk; Model 2 report results when the risk is measured by systematic risk and Model 3 report results when the risk is measured by idiosyncratic risk. lnVega is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock return volatility. lnDelta is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock price. lnAssets is the natural log of total bank assets; Market to book is the bank’s market-to-book ratio of equity; Equity Ratio is total equity capital over total assets.. ***, **, * Represent significance at the 1%,5% and 10% levels respectively. Robust standard errors are shown in parentheses under the coefficients.
(1) (2) (3)
Total Risk Systematic Risk Idiosyncratic Risk Panel A Constant -0.00102 1.184 -0.00767 (0.0585) (1.867) (0.0551) lnVegai,t-1 0.00422*** 0.0919** 0.00331** (0.00147) (0.0430) (0.00143) lnDelta i,t-1 -0.00505** -0.151*** -0.00456** (0.00193) (0.0389) (0.00185) LnAssets i,t-1 0.00344 0.0881 0.00344 (0.00315) (0.100) (0.00303)
Market to book i,t-1 -0.00798** -0.227* -0.00713***
(0.00319) (0.115) (0.00249)
Equity ratio i,t-1 -0.142* -4.597** -0.131*
(0.0799) (2.030) (0.0753)
Year dummy’s Yes Yes Yes
Observations 288 288 288 R-squared 0.866 0.705 0.810 Number of banks 66 66 66 Panel B Constant -0.0220 -0.858 -0.00730 (0.0608) (2.927) (0.0565) lnVegai,t-1 0.000772 0.0475 0.000724 (0.000611) (0.0326) (0.000523) lnDelta i,t-1 -0.00200* -0.0791** -0.00213** (0.00109) (0.0337) (0.000956) LnAssets i,t-1 0.00573 0.164 0.00466 (0.00367) (0.182) (0.00353)
Market to book i,t-1 -0.00923*** -0.0512 -0.00942***
(0.00249) (0.0574) (0.00210)
Equity ratio i,t-1 -0.190*** 0.699 -0.217***
(0.0553) (1.485) (0.0507)
Year dummy’s Yes Yes Yes
Observations 218 218 218
R-squared 0.848 0.531 0.789
22 The regulation effect
This section will specifically look at how the effects of vega and delta on bank risk have developed in the years subsequent to the financial crisis with the implementation of the Dodd Frank Act as focal point. This massive and complex regulatory initiative has revamped securitization rules; changed the oversight of derivatives; changed the prudential standards for risk-based capital, leverage, liquidity, and contingent capital; imposed the Volcker Rule, contains provisions for corporate governance and led to the creation of new regulatory agencies. As banks and its CEO’s will need to comply with these new rules and changes in requirements this limits their risk-taking possibilities and hence might mitigate the effect of incentive based compensation.
23 Table 5: This table shows the results of OLS estimations with inclusion of firm-fixed and time-fixed effects for the 2006-2014 period. Since I work with a 1-year lag, the dependent variables used are for the 2007-2014 period, and the independent variables are for the 2006–2013 period. Model 1 report results when the risk is measured by total risk; Model 2 report results when the risk is measured by systematic risk and Model 3 report results when the risk is measured by idiosyncratic risk. lnVega is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock return volatility. lnDelta is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock price. Vega*regulation is vega times the dummy variable regulation (which takes on a value 0 for the 2006-2010 period and a value 1 for the 2011-2014 period) which measures the change in effect of vega on risk taking post regulation. lnAssets is the natural log of total bank assets; Market to book is the bank’s market-to-book ratio of equity; Equity Ratio is total equity capital over total assets.. ***, **, * Represent significance at the 1%,5% and 10% levels respectively. Robust standard errors are shown in parentheses under the coefficients.
(1) (2) (3)
Total risk Systematic risk Idiosyncratic risk
Constant -0.0534 -1.270 -0.0361
(0.0382) (1.545) (0.0362)
lnVegai,t-1 0.00115** 0.0490** 0.00109**
(0.000529) (0.0232) (0.000473)
lnVega* regulationi,t-1 -5.73e-06*** -0.000208*** -3.67e-06***
(1.25e-06) (5.29e-05) (1.16e-06)
lnDelta i,t-1 -0.00269** -0.108*** -0.00267***
(0.00107) (0.0286) (0.000942)
LnAssets i,t-1 0.00691*** 0.199** 0.00566***
(0.00223) (0.0918) (0.00214)
Market to book i,t-1 -0.00746*** -0.103* -0.00758***
(0.00184) (0.0527) (0.00155)
Equity ratio i,t-1 -0.149*** -0.560 -0.165***
24 Table 6: This table shows the results of OLS estimations with inclusion of firm-fixed and time-fixed effects for the 2006-2014 period. Since I work with a 1-year lag, the dependent variables used are for the 2007-2014 period, and the independent variables are for the 2006–2013 period. Model 1 report results when the risk is measured by total risk; Model 2 report results when the risk is measured by systematic risk and Model 3 report results when the risk is measured by idiosyncratic risk. lnVega is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock return volatility. lnDelta is measured as the natural log of the sensitivity of a CEO’s wealth to a 1% increase in stock price. Delta*regulation is delta times the dummy variable regulation (which takes on a value 0 for the 2006-2010 period and a value 1 for the 2011-2014 period) which measures the change in effect of delta on risk taking post regulation. lnAssets is the natural log of total bank assets; Market to book is the bank’s market-to-book ratio of equity; Equity Ratio is total equity capital over total assets.. ***, **, * Represent significance at the 1%,5% and 10% levels respectively. Robust standard errors are shown in parentheses under the coefficients.
(1) (2) (3)
Total risk Systematic risk Idiosyncratic risk
Constant -0.0438 -0.949 -0.0293 (0.0390) (1.572) (0.0365) lnVegai,t-1 0.00111** 0.0474** 0.00106** (0.000546) (0.0237) (0.000483) lnDelta i,t-1 -0.00278** -0.111*** -0.00274*** (0.00108) (0.0288) (0.000955)
lnDelta* regulationi,t-1 -1.16e-06 -4.66e-05* -6.41e-07
(7.67e-07) (2.74e-05) (6.41e-07)
LnAssets i,t-1 0.00632*** 0.179* 0.00524**
(0.00227) (0.0932) (0.00215)
Market to book i,t-1 -0.00729*** -0.0968* -0.00747***
(0.00191) (0.0547) (0.00158)
Equity ratio i,t-1 -0.142*** -0.338 -0.160***
25 Table 6 presents the results of the regression model with the inclusion of the delta*regulation interaction variable. Columns 1,2 and 3 show that the results for the effect of vega on the different risk measures are similar to the results of the original model as presented in table 3. As opposed to the vega*regulation interaction I find no strong statistical significant coefficients for the delta*regulation interaction variable. I only find a weak negative statistical significant coefficient (at the 10% level) for the delta interaction variable when risk is measured by systematic risk. The delta*regulation interaction variable coefficients for the other risk measures are not statistically significant. Indicating that the delta coefficients have not significantly changed in 2011-2014 compared to the full sample period 2006-2014 when risk is measured by total risk or idiosyncratic risk. Meaning that the negative effect delta has on risk has not significantly changed with the implementation of the Dodd Frank Act. Although figure 3 shows a decrease in the level of delta during the financial crisis it shows an increase in delta from 2011 onwards9. This could explain that the reduction in the effect of delta on bank risk does not significantly differ in 2011-2014 compared to the full sample period 2006-2014. Moreover, Coles, Daniel, and Naveen (2006)argue that vega can potentially reduce a CEO’s aversion to risky policies that arise from high delta. Hence a reduced level of vega might contrarily increase the aversion to risky policies by CEO’s that arise from delta.
5. Conclusion
The effect of executive ownership and compensation structure on performance and risk-taking in the banking industry is a topic of importance to academics, practitioners, and particularly to regulators. By using a dataset of 105 banks this study is among the first to examine the effect of CEO wealth incentives on bank risk in the years during and subsequent to the financial crisis in the US.
Overall I find that bank CEO’s experienced lower levels of vega and delta in the period subsequent to the financial crisis. Despite this decline I find that banks in which CEO’s experience a higher vega exhibit larger amounts of stock return volatility, systematic risk and idiosyncratic risk. These effects are primarily driven by observations in which CEO’s experience a high wealth sensitivity to risk as compared to their total cash compensation. Suggesting that bank boards need to provide CEO’s with a minimum level of vega compared to a CEO’s total cash compensation in order to incentivize them to pursue riskier business policies. In line with the expected relation from the principal agent model I find that banks in which CEO’s receive a higher delta exhibit substantially lower amounts of stock
9
26 return volatility, systematic risk and idiosyncratic risk. Combined , these results implicate that banks can effectively manage the risk-taking by a CEO through the use of incentive based compensation. John, Saunders, and Senbet (2000) extend this argument and suggest that incentive features of top management compensation, such as the sensitivity of pay to performance, be used as an input in bank regulation and in the calculation of FDIC insurance premiums. They argue that a regulatory framework that accounts for the incentives of top managers will be more efficient than capital regulation in curbing their risk-shifting incentives.
Using interaction variables I test for the difference of the wealth sensitivity effects on risk before and after the implementation of the Dodd Frank Act. From these regressions I find that the vega effect on risk-taking has reduced in the years subsequent to this major legislative change. Contrary to the diminishing vega effect I do not find any change in the effect of delta on bank risk after the implementation of the Dodd Frank Act. Implicating that bank boards have reduced the incentive for CEO’s to induce in higher risk through the use of vega in a regulated environment with limited growth opportunities and increased disclosure requirements.
6. Discussion
One key limitation in this research is that I cannot make causal inferences on the effect of the Dodd Frank Act on compensation and bank risk. In my conclusion I argue that the regulatory changes post 2010 have reduced the positive effect of vega on taking. This reducing effect of vega on risk-taking might however also be related to the difference in volatility between the financial crisis and the years subsequent to the financial crisis. As can be seen from figure 1, on average, stock return volatility reduced significantly in the years 2011-2014 compared to the volatile 2006-2010 period. When data on more years is available the mitigating effect of regulation on the relation between vega and risk-taking should be researched without inclusion of the volatile financial crisis period as this might contaminate results.
27 Similar to previous researches10 I am limited to a relatively small sample of banks for which full compensation data is available. These small sample might bias results and overstate the effect of outliers. Moreover, In this research I only look at the relation between CEO wealth incentives and a bank’s market based risk measures. Further research should also look into how this risk was built up over different asset classes. This will give further insight through which policies decisions CEO’s influenced bank risk.
Finally a limitation to this study is that I do not examine the reverse effect risk has on the level of wealth sensitivities. Whereas my used model assumes that my explanatory variables determine risk, it is also possible that causation works the other way around, as risk might influence the level of CEO vega and delta set by bank boards. In order to isolate this causation and avoid spurious inferences Coles et al (2006) state that the empirical design needs to disentangle how compensation and incentives affect policy and risk from how policy and the corresponding risk profile of the firm’s assets affect the compensation scheme of a risk averse manager. By using lagged values of vega and including fixed effects my research design mitigates this endogeneity concern. Previous researches (DeYoung et al 2013, Bai & Elyasiani 2013) are however more actively addressing these possible endogeneity issues by setting up a simultaneous equation model and using instrumental variables for risk and vega.
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8. Appendices
Appendix I: CalculatingBlack-Scholes value and sensitivities of individual stock options
Estimates of a stock option's value or sensitivity to stock price or stock return volatility are calculated based on the Black-Scholes [1973] formula for valuing European call options, as modified to account for dividend payouts by Merton [1973].
Option value = [Se-dT N(Z) – Xe-rT N(Z – σ T(1/2))], where
Z = [ln(S/X) + T(r – d + σ2/2)] / σ T(1/2)
N = cumulative probability function for the normal distribution S = price of the underlying stock
X = exercise price of the option
σ = expected stock-return volatility over the life of the option r = natural logarithm of risk-free interest rate
T = time to maturity of the option in years
d = natural logarithm of expected dividend yield over the life of the option
The sensitivity with respect to a 1% change in stock price(delta) is defined as: [ 𝜕(option value)/ 𝜕 (price) * (price/100) = e-dT N(Z) * (price/100)
The sensitivity with respect to a 0.01 change in stock-return volatility(vega) is defined as: [𝜕 (option value) / 𝜕 (stock volatility)] * 0.01 = e-dT N’ (Z) ST(1/2) * (0.01),
31 Appendix II: Correlation matrix
Std(Stock Return) i,t Beta(market) i,t Std (residual) i,t
Vega i.t-1 Delta i.t-1 Total assets i.t-1 Lnassets i.t-1
CAR i.t-1 Market
to book i.t-1 Regulation i.t Vega * regulation i.t-1 Delta * regulation i.t-1 Std(Stock Return) 1 Beta(market) 0.5867 1 (0.00) Std (residual) 0.9746 0.4884 1 (0.00) (0.00) Vegai.t-1 -0.002211 0.0902 -0.0511 1 (0.96) (0.0317) (0.22) Deltai.t-1 -0.0681 -0.0366 -0.1029 0.7676 1 (0.10) (0.3838) (0.01) (0.00)
Total assets i.t-1 0.0219 0.2017 -0.0206 0.4337 0.3705 1
(0.60) (0.00) (0.62) (0.00) (0.00)
Lnassetsi.t-1 -0.0263 0.1851 -0.0824 0.5378 0.4732 0.7235 1
(0.53) (0.00) (0.05) (0.00) (0.00) (0.00)
CARi.t-1 -0.1971 -0.0577 -0.2172 -0.0165 -0.0023 -0.128 -0.0541 1
(0.00) 0.1699 (0.00) (0.70) (0.96) (0.00) (0.20)
Market to booki.t-1 -0.1596 -0.1907 -0.1976 0.0624 0.0964 -0.1802 -0.2012 -0.1694 1
(0.00) (0.00) (0.00) (0.14) (0.02) (0.00) (0.00) (0.00) regulation -0.4497 -0.3133 -0.4136 -0.0941 -0.0792 0.0461 0.0809 0.1817 -0.3599 1 (0.00) (0.00) (0.00) (0.02) (0.06) (0.27) (0.05) (0.00) (0.00) Vega*regulation i.t-1 -0.2001 -0.1058 -0.2088 0.5426 0.4457 0.3381 0.4126 0.0087 -0.0801 0.2208 1 (0.00) 0.0116 (0.00) (0.00) (0.00) (0.00) (0.00) (0.84) (0.06) (0.00) Delta*regulation i.t-1 -0.2085 -0.1357 -0.2123 0.38 0.6233 0.2678 0.3382 0.0363 -0.0585 0.2319 0.7443 1 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.39) (0.16) (0.00) (0.00) 11
32 Appendix III: Development of EBC in CEO compensation contracts
Figure 4: The yearly average number of stock and option holdings for bank CEO’s (681 observations) from 2006-2014.
Appendix IV: The level of vega in the banking industry compared to the level of vega industrial firms
33 Appendix V: The level of delta in the banking industry compared to the level of delta industrial firms
