- Email: [email protected]
Do bank CEOs really increase risk in vega? Evidence from a dynamic panel GMM specification
Accepted Manuscript Title: Do bank CEOs really increase risk in vega? Evidence from a dynamic panel GMM specification Authors: Rakesh Bharati, Jingyi Jia PII: DOI: Reference:
S0148-6195(17)30080-2 https://doi.org/10.1016/j.jeconbus.2018.06.001 JEB 5812
To appear in:
Journal of Economics and Business
Received date: Revised date: Accepted date:
28-3-2017 1-6-2018 5-6-2018
Please cite this article as: Bharati R, Jia J, Do bank CEOs really increase risk in vega? Evidence from a dynamic panel GMM specification, Journal of Economics and Business (2018), https://doi.org/10.1016/j.jeconbus.2018.06.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Do bank CEOs really increase risk in vega? Evidence from a dynamic panel GMM specification1
SC RI PT
Rakesh Bharati, Jingyi Jia Rakesh Bharati Professor, Department of Economics and Finance, School of Business, Southern Illinois University – Edwardsville, Edwardsville, IL 62026, Email: [email protected], Tel: 618-650-2549
N
U
Jingyi Jia (Corresponding Author) Associate Professor Department of Economics and Finance, School of Business, Southern Illinois University – Edwardsville, Edwardsville, IL 62026, Email: [email protected], Tel:618-6502980
M
A
March 23, 2018
A
CC
No evidence for positive risk -CEO compensation vega relationship Strong evidence for positive risk - CEO compensation delta relationship Delta relation is driven by low-leverage banks which are less risk-averse. Delta relation is not in commercial banks and high-leverage bank.
EP
TE
D
Highlights
1
We sincerely appreciate the constructive comments and suggestions of the editor and two anonymous referees to help us improve the paper. 1
Abstract:
M
A
N
U
SC RI PT
Previous executive compensation studies find that firm risk increases in the risk-taking incentive (vega) of CEOs’ compensation packages. However, the standard methodology of two-stage least squares (2SLS) regression can suffer from invalid instruments. Using a dynamic panel generalized method of moments (GMM) specification to control for dynamic endogeneity, unobserved heterogeneity, and simultaneity (Wintoki, et al., 2012), we find no evidence of a positive relationship between risk and vega for banking firms. Furthermore, across institutions, CEOs’ payperformance sensitivity (delta) positively relates to the risk. Finally, high-leverage banks and commercial banks seem less prone to risk increases in delta relative to the entire sample of financial institutions. These results are important to investors, boards, regulators, and creditors, as they are all concerned with the risk of the financial institution.
CC
EP
1. Introduction
TE
D
Key words: CEO Compensation, Dynamic Panel GMM model, bank risk-taking JEL Classification: G21; G28; G32; G34; J33
Vega is the sensitivity of a CEO’s compensation to the risk of her firm’s stock and it is calculated
A
as the change in dollar CEO compensation for a one percent change in the annualized standard deviation of stock returns (Core and Guay, 2002). Delta, or pay-performance sensitivity, is the marginal impact of stock price changes on CEO compensation. Delta is calculated as the change in dollar CEO compensation for a one percent change in the stock price. The relationship between 2
risk-taking and CEO compensation (vega and delta) has profound implications for the entire economic system, including bank boards, capital providers, and regulators. Bank regulators such as Federal Reserve Bank (FRB) and the Federal Deposit Insurance Corporation (FDIC) need to
SC RI PT
monitor the CEO compensation for the safety and soundness of the banking system and economy. CEOs take less than optimal risk when given inadequate incentives for risk-bearing, while aggressive incentives result in excessive risk-taking. Both outcomes, if systemic, are economically undesirable, as they can result either in low economic growth, or in widespread financial distress and recession.2 If this relationship is not well understood, bank boards may be incorrectly using
U
vega and delta in the CEO compensation package decision to control the bank’s risk, and investors
N
and bond-rating agencies may also be overweighting vega in determining the institution’s risk.
A
Empirically, the limited evidence on compensation and bank risk is mixed. 3 With two-stage least
M
squares (2SLS) regression method, DeYoung, et al. (2013) document that banks where CEOs had high vega compensation took substantially large amounts of both systematic risk and unsystematic
D
risk during 1995-2006. However, Fahlenbrach and Stulz (2011) find bank performance during the
TE
financial crisis to be unrelated to CEOs’ vegas at the end of 2006. The evidence on risk-delta
EP
relationship is ambiguous too (Armstrong and Vashishtha, 2012; Coles et al., 2006; Fahlenbrach and Stulz, 2011).
CC
There is justification for the skepticism of standard models like 2SLS in the risk-incentive context.
A
Instrument validity is a concern in the highly endogenous environment of risk-governance and the
Accordingly, Basel Committee for Banking Supervision notes that “compensation systems contribute to bank performance and risk-taking, and should therefore be key components of a bank’s governance and risk management [Principles for Enhancing Corporate Governance, October 2010]. 3 For banks, Bai and Elyasiani (2013) also provide support for a positive risk-vega relation. For the corporate sample, multiple studies find a positive risk-vega relationship (Amadeus and Sadka, 2015; Anantharaman and Lee, 2014; Coles, et al., 2006; and Hagendorff and Vallascas, 2011). 2
3
economy, because the instrumental variables affecting risk through compensation are also very likely to affect risk directly. Second, simultaneous equation models cannot fully address the dynamic endogeneity between risk and compensation variables. This occurs when lagged values
SC RI PT
of risk affect the present compensation, and the present compensation affects the future risk. We study the risk-vega relationship using a dynamic panel generalized method of moments (GMM) specification motivated by Arellano and Bond (1991), and employed in a performance-
governance context by Wintoki et al. (2012). The key advantage of the model is that with predetermined variables (e.g., lagged variables) as instruments, strictly exogenous instruments are
U
not necessary. The model has the added advantage of addressing dynamic endogenity by including
N
lagged dependent variables in the regressors. In addition, the GMM approach provides formal
M
Difference-in-Hansen test of exogeneity).
A
tests of the validity and exogeneity of the instruments (Hansen’s test of over-identification and
D
We find no evidence supporting a significant risk-vega relationship. In particular, the positive
TE
risk-vega relationship is insignificant for total and systematic risk, and only marginally positive for unsystematic risk. Clearly, a correction of dynamic endogeneity yields different results from
EP
those with 2SLS regressions. The evidence of a positive risk-vega relationship found in corporate
CC
studies may not apply here, as banks are regulated and have high leverages.4 Another potential
A
reason for the insignificant risk-vega relationship is that most stock options held by bank CEOs
4
We would like to thank an anonymous referee for the suggestion to clarify the effect of leverage on risk-taking. First, risk-taking may decrease at high leverage levels due to the risk-aversion of the CEO (Carpenter, 2000; Lewellen, 2006). Second, high bank leverage may prompt bondholders to actively perform monitoring which may reduce risktaking in vega (John and Qian, 2003; and John et al., 2010). We are also aware that high leverage in the banking industry may lead equity holders to invest in very risky projects and provide CEOs with more stock and stock options to incentivize risk-taking (Ross et al., 2010; Harris and Raviv, 1991). 4
are well-in-the-money, making the CEOs more conservative in risk-taking (Fahlenbrach and Stulz (2011). Our second finding is that delta is positively associated with risk-taking across all risk categories,
SC RI PT
consistent with Fahlenbrach and Stulz (2011) in banking studies and Armstrong and Vashishtha (2012) in corporate studies. Therefore, a greater sensitivity of a CEO’s wealth to stock price motivates the CEO to take higher risk to improve the bank’s long-term performance, as this would improve the stock price and the CEO’s personal wealth. 5 This positive risk-delta relationship could be attributable to an expectation that the government will not let banks fail (too-big-to-fail
U
problem) and bank stock is similar to a call option, as the downside risk is eliminated or reduced.
N
Further, consistent with the theoretical prediction, we find that high leverage banks appear less
A
likely to increase risk in delta, compared to low leverage banks (e.g., Booth, et al., 2002; Lewellen,
M
2006; John, et al., 2010). Commercial banks also share this reduced propensity to risk taking in
D
delta. This can be viewed as a reconciliation of our results on delta with those in DeYoung et al.
TE
(2013) since that study is based on commercial bank sample. Our results are critically important to bank regulators, boards, and investors. Based on our
EP
findings, the FDIC must include compensation delta when pricing deposit insurance for a bank,
CC
and FRB should consider delta when auditing banks to detect excessive risk-taking. Bank boards should pay more attention to CEO compensation delta and they should not overly rely on
A
compensation vega to motivate the CEO to take the optimal level of risk. Bond rating agencies
Fahlenbrach and Stulz (2011) mentions (Page 12) that if CEO’s holdings of stock make him more conservative, higher vega would help in aligning the CEO’s incentives with those of shareholders by increasing risk. Since we find that delta mainly driven by stock holdings is still positively related to risk, it seems that CEOs are not at the stage of being conservative and the effect of vega is not very obvious. 5
5
and investors should also make use of the information in compensation delta to rate bank bonds and to trade bank stocks. Following the literature review in Section 2, hypothesis development and methodology are
SC RI PT
explained in Section 3. Data and the sample are described in Section 4. Primary results are presented in Section 5. In Section 6, we investigate the influence of bank characteristics. Section 7 concludes the paper. 2. Literature review
U
2.1. Theory and evidence on executive compensation
N
Compensation structure includes vega, delta, cash compensation, and other variables (e.g., pension
A
and other benefits). Core-Guay (1999, 2002) employ a one-year approximation method to
M
compute compensation package sensitivities. Vega represents the convexity of the compensation
D
package that incentivizes risk-taking. There are good reasons to doubt a universally positive risk-
TE
vega relationship. First, a positive risk-vega relationship is a comparative static of the BlackScholes option pricing model, which is derived under perfect, costless hedging, leading to a risk
EP
neutral valuation – assumptions that may not apply to a typical risk-averse CEO who may be trading and hedging constrained due to corporate policies, regulatory structures, and insider trading
CC
rules.6 Second, under managerial risk aversion, vega may be risk reducing or increasing depending
A
upon the moneyness of the options (e.g., Lambert, et al., 1991; Carpenter, 2000; Ross, 2004; Parrino et al., 2005; Lewellen, 2006). Specific to banks, regulatory supervision may curb
6
Early exercise of options, after vesting but long before their actual maturity, strongly support executive risk aversion (e.g., Huddart and Lang, 1996; Hemmer et al., 1996; Heath, et al., 1999; Hall and Murphy, 2002; Bettis et al., 2005). 6
independence and make risk-taking incentives less important or irrelevant (e.g., Booth, et al., 2002; John et al., 2000), as it could invite stronger regulatory scrutiny. The highly leveraged nature of banks prompts bondholders to actively perform monitoring, which may reduce risk-taking (e.g.,
SC RI PT
John and Qian, 2003; and John, et al., 2010). Also, banks that trade derivatives need high credit ratings, which may reduce risk-taking (Fahlenbrach and Stulz, 2011).
Empirically, using 2SLS modeling, Bai and Elyasiani (2013) find a positive relationship between vega and the insolvency risk proxied by the Z-Score. Similarly, DeYoung, et al. (2013) support a positive risk-vega relationship and find evidence of some implementation of risk policies in vega.
U
Hagendorff and Vallascas (2011) show that risky bank acquisitions increase in vega. Whereas the
N
above studies support the positive relationship, Fahlenbrach and Stulz (2011) focus on the crisis
A
years and show that CEO compensation vega across banks does not explain market or accounting
M
based performance measures – equity return, return on assets, and return on equity.
D
Delta could be risk enhancing, risk reducing, or neutral (Chava and Purnanandam, 2010;
TE
Fahlenbrach and Stulz, 2011; DeYoung et al., 2013; Berger, et al., 2016). On the one hand, highdelta compensation from large stock grants will align the interest of shareholders and the CEO,
EP
inducing higher risk-taking (Jensen and Meckling, 1976; John and John, 1993). In addition, the
CC
guarantee provided by FDIC may induce the CEO to prefer higher risk with higher delta compensation. On the other hand, a high delta may increase the wealth concentration of a CEO in
A
the firm’s stock, and induce greater risk aversion through non-diversifiable human capital. The evidence on risk-delta relation is ambiguous with Armstrong and Vashishtha (2012), Coles et al. (2006), and Fahlenbrach and Stulz (2011) producing supportive evidence for a positive
7
relationship, while Chava and Purnanadam (2010)
and DeYoung, et al.(2013) produce
contradictory results. Cash compensation, including cash salary and bonus, also has two conflicting effects on risk-
SC RI PT
taking (Guay, 1999; Coles et al., 2006). Berger et al. (1997) show that higher CEO cash compensation is associated with a lower leverage ratio and lower risk because the CEO wants to protect non-diversifiable human capital. However, Guay (1999) argues that cash compensation can be invested outside of the firm. Thus, the CEO is more diversified and may prefer higher risk
U
with higher cash compensation.
N
2.2. Methodological approaches employed in extant literature
A
Based on the insights offered by Wintoki et al. (2012) in the performance-governance relationship,
M
estimation of the risk-vega relationship entails three kinds of endogeneity issues: unobservable heterogeneity, simultaneity, and dynamic endogeneity. The following discusses the advantages of
TE
D
the dynamic GMM model in addressing these issues relative to other methodologies.
EP
2.2.1. Fixed-effects estimation to address unobservable heterogeneity Unobservable heterogeneity occurs when an omitted factor (e.g., managerial ability) affects both
CC
the dependent variable (risk-taking in our case) and the independent variable of interest (vega), and is commonly remedied through the use of fixed-effects estimation (e.g., Hermalin and
A
Weisbach, 1991; Himmelberg et al., 1999). 7 Given dynamic endogeneity, the fixed-effects estimation is not consistent and can reduce the power of the tests and produce biased estimation.
7
Himmelberg et al. (1999) show that regression of firm performance on firm policy or characteristics (or vice versa) may lead to spurious regression, as they are endogenously determined and that the exogenous variables (e.g., managerial abilities) crucial to the determination are not observable. Therefore, correction for endogeneity is critical. 8
This is because the assumption that current observations of the explanatory variable (vega and delta) are independent of past values of the dependent variable (risk variables) is not realistic (Wintoki et al., 2012). Compared to the fixed-effects regression model, the dynamic GMM panel
SC RI PT
specification produces unbiased estimates if there is a dynamic relationship between independent variables and lagged dependent variables. The dynamic GMM model accounts for unobservable heterogeneity by including firm fixed-effects in the model specification. 2.2.2. Simultaneous equations model to address simultaneity
U
Simultaneity occurs when the variables of interest (risk-taking and vega) are jointly determined,
N
and it is addressed through a simultaneous equation model (e.g., Rajgopal and Shevlin, 2002; Coles
A
et al., 2006; Armstrong and Vashistha, 2012; DeYoung, et al., 2013; Bai and Elyasiani, 2013).
M
Simultaneous equations models, though attractive, require strictly exogenous instruments that are very difficult to identify in a corporate finance setting where theory provides little guidance, as is
D
the case of executive compensation. For instance, Coles et al. (2006) use lagged and predicted
TE
values of vega and delta as exogenous instruments to address the endogeneity. By contrast, DeYoung et al. (2013) employ the following instruments – economic conditions, transient
EP
institutional ownership, past cumulative returns, salary, and tenure. While these variables may be
CC
related to vega and delta, it is difficult to argue that they have no direct influence on bank risk.
A
This possibility compromises their use as instruments.8
8
Some studies use the natural experiment approach to resolve the issue of endogeneity (e.g., Delaware Supreme Court’s 1995 Unitrin Inc. v. American General Corp. ruling that increased takeover protection in Low (2009)). Nevertheless, this approach comes with its own set of complications because natural experiments may not be truly exogenous. For example, regulatory or other changes may be designed specifically to obtain a certain outcome. Further, the changes could be anticipated, allowing for the environment and expectations to adjust. Indeed, Chava and Purnanandam (2010) and Hayes et al. (2012) reach different conclusions after conditioning on the 2004 FASB ruling on option expensing. 9
By contrast, the dynamic GMM model uses lagged dependent and independent variables as instruments. It essentially constrains the researcher from using an arbitrary set of instruments, which may just happen to be correlated with the variables of interest. Further, the approach
SC RI PT
provides formal tests of the validity and exogeneity of instruments, namely Hansen’s test of overidentification and the Diff-in-Hansen test. Similar tests are not formalized for simultaneous equation models. The dynamic GMM approach is also robust to heteroscedasticity and serial correlation, unlike the 2SLS approach.
U
2.2.3. Dynamic GMM model to address dynamic endogeneity
N
Dynamic endogeneity has heretofore been unaddressed in executive compensation studies. The
A
problem is caused by the dependence of the independent variables (vega or delta) on the lagged
M
values of the dependent variable (risk-taking) in the presence of unobservable effects (Wintoki et al., 2012). Using a dynamic panel GMM model originally motivated by Arellano and Bond (1991)
D
to account for dynamic and other forms of endogeneity, Wintoki et al. (2012) find no relationship
TE
between performance and board structure, unlike prior studies.
EP
Intuition suggests that dynamic endogeneity also exists in the relationship of risk-taking and CEO incentive compensation because compensation committees will structure the CEO compensation
CC
measures, such as vega or delta, based on the past risk level. Further, the performance goals and compensation structure are set through discussions between the board and the CEO, and her
A
bargaining position is affected by the past bank risk. Indeed, Pathan (2009) presents evidence that CEO power, measured through CEO duality and the founder or internal-hire status, is negatively related to bank risk-taking. DeYoung, et al. (2013) argue that bank boards take existing levels of market risk into consideration when they set CEO wealth incentives. 10
It is also empirically known that there is a degree of persistence in the bank (or corporate) performance measures, and Wintoki et al. (2012) uses lags of the dependent variables as controls to ensure a robust specification. Indeed, it is increasingly common to use a dynamic specification
SC RI PT
for bank risk. 9 Assuming compensation’s dependence on the past risk, the failure to include persistent lagged risk can lead to its effect being captured by the compensation structure variables, resulting in incorrect conclusions. 3. Hypothesis development and the econometric model
U
In the 1990s, compensation incentives became more relevant to the banking industry (Crawford,
N
et al., 1995; Hubbard and Palia, 1995) with the financial deregulation and rapid expansion of
A
banks.10 As DeYoung at al. (2013) show, while the average total compensation remained slightly
M
above that of non-banking firms, the dollar vega value of a CEO compensation contract increased rapidly relative to non-banks after 1994, peaked around 2003, and maintained this substantial
D
spread until 2006. This run-up partly supported the popular opinion that bank compensation
TE
practices were at least partly to blame for the excessive risk taking and the subsequent financial
EP
crisis.
We propose and test a relationship between the market measures of risk and the previous year
9
CC
compensation structure variables (vega, delta, and cash compensation) for banks. This lead-lag
A
Delis and Kouretas (2011) use a dynamic specification of risk in their study of bank risk and competition, where risk is measured as the nonperforming loan ratio. Ellul and Yerramilli (2013) use a dynamic panel GMM approach to model bank tail risk. Fiordelisi et al. (2011) also use lags of the nonperforming loan ratio, in addition to lagged expected default frequency. Koutsomanoli-Filippaki and Mamatzakis (2009) use the dynamic panel GMM to model the distance-to-default for a sample of European banks. 10 In the 1990s, the banking industry saw two major regulatory overhauls. First, the Riegle-Neal Interstate Banking and Branching Efficiency Act of 1994 was a step towards nation-wide banking, as restrictions on expansion across state line were eased. Next, by effectively repealing the ownership restrictions on bank holding companies, the Gramm-Leach-Bliley Financial Services Modernization Act of 1999 permitted entry into formerly excluded lines of business (e.g., brokerage and fund management, investment banking, and insurance). 11
relation is similar to Rajgopal and Shevlin (2002) and DeYoung et al. (2013). On the other hand, the lead-lag relation is different from Coles et al. (2006), who present results from a simultaneous specification of risk policies and compensation sensitivities. However, in their Table 9, they do
SC RI PT
present total risk regressed on lagged sensitivities as a robustness test. The advantage of this lead risk, lagged compensation structure specification is that it allows the implemented risk policies to influence the market perception of risk.
Our literature review discussion in Section 2 suggests that a positive risk-vega relationship may not exist for banks and the two other major components of the compensation structure – delta and
U
cash compensation – can be risk-decreasing or risk-enhancing. Also, cash compensation and delta,
N
with a few exceptions for delta, are usually employed in other studies as control variables, but we
A
treat them as variables of interest. This is consistent with the studies that indicate that boards may
M
be reluctant to reduce vega and may temper the CEO’s risk appetite with other components of the
TE
our hypothesis below.
D
compensation structure (e.g., DeYoung et al. (2013) on the use of delta). Therefore, we propose
EP
H1: Bank risk is unrelated to CEO compensation structure (vega, delta, and cash compensation). The Arellano and Bond (1991) methodology differences the original level equation, and then
CC
estimates the differenced equation with predetermined instruments in levels. However, as Wintoki et al. (2012) note, differencing may reduce variation in the data and decrease the power of the test,
A
and can make the measurement error problem more severe. Further, variables in levels may make weak instruments for the first-differenced equation. To address these potential shortcomings, the level equation is also included with the differenced equation in a system GMM model (Arellano
12
and Bover, 1995; Blundell and Bond, 1998). The first-differenced variables are the instruments for the equations in level. The estimated system GMM model is as follows:
SC RI PT
𝐸 (1) 𝑌 𝑌 𝑋 𝑍 ( 𝑡 ) = 𝛼 + 𝛽 ∗ ( 𝑡−𝑘 ) + 𝛾 ∗ ( 𝑡−1 ) + 𝛿 ∗ ( 𝑡 ) + 𝑡 𝑦𝑡 𝑦𝑡−𝑘 𝑥𝑡−1 𝑧𝑡 𝜀𝑡 (2) Y is the level dependent variable (the measure of risk in this study) and y is the first difference of Y (the risk measure less its one lag). X and x, in a similar fashion, indicate the level and the first difference of the independent variable (vega, delta and cash compensation in our case). The presence of minus one in the subscript of X and x indicates that current year’s risk measure is
U
being regressed on the explanatory variables at the end of the previous year. is the coefficient
N
that is hypothesized to be zero under H1 above. Z and z similarly indicate the control variables,
A
which include CEO age, CEO tenure, logarithm of market capitalization, book leverage ratio,
M
ROA and year dummies. 11 Finally, is an independently and identically distributed normal
D
variate with a zero mean, and its lower case counterpart () is its first difference. Note that the
EP
specification.
TE
model includes lagged dependent variables up to k further lags to account for a dynamic
The GMM instruments for the first-differenced equation include lagged levels of vega, delta and
CC
cash compensation older than two years (three years ago and further).12 The GMM instruments for the level equation are lagged differences of these three compensation variables older than one year
A
(two years ago and further). In our GMM estimation, following Wintoki (2012), we use the twostep estimation option to achieve greater asymptotic efficiency, compared to the one-step
11
Similar to Appendix B in Wintoki et al.(2012), these variables are the exogenous partition of the independent variables. In STATA, these variables are included in ivstyle( ), and called standard instruments. 12 Similar to Appendix B in Wintoki et al.(2012), these variables are the endogenous partition of the independent variables. In STATA, these variables are included in gmmsyle( ), and called GMM style instruments. 13
estimation option. We also use the robustness option to implement the finite-sample correction
SC RI PT
procedure (Windmeijer, 2005).13
4. Data, sampling and variable construction 4.1. Data
CEO related variables are from Standard and Poor’s ExecuComp database for banking firms (SIC
U
codes of 6020 for commercial banks, 6035 for federally chartered saving institutions, and 6036 for
N
state-chartered saving institutions). This data provides the information to construct vega and delta
A
for the sample period of 1993-2009. Stock volatility over the past five years and dividend yield
M
over the past three months are not available in the database after 2006 due to a change in SEC
D
reporting requirements. Therefore, we construct these two variables for the latter period using
TE
Standard and Poor’s methodologies.14 We construct bank risk measures (total, systematic, and unsystematic risk) with data from the Center for Research in Security Prices (CRSP). Other firm
EP
control variables are constructed from COMPUSTAT. The final sample used in the estimations has 1521 observations from 217 banks with complete data during 1993-2009. All GMM estimates
CC
are based on 1058 observations from 15 years (1995 – 2009). Observations from 1993 and 1994
A
are omitted due to the differencing.
13
For example, we use the following code for the estimation of the total risk model: xtabond2 risk_total l.risk_total l2.risk_total vega delta total_curr tenure age log(MV) Market/Book bookleverage ROA year_1993-year_2009, gmm(vega delta total_curr, lag (3 . ) collapse) iv(age tenure log(MV) Market/Book bookleverage ROA year_1994year_2009) twostep robust small. 14 We sincerely appreciate detailed instructions and great help from Lindsey Fenner, the senior product consultant from Standard and Poor’s. 14
4.2. Variable construction and descriptive statistics Our analysis employs three sets of variables, for which the descriptive statistics are presented in Table 1.
SC RI PT
4.2.1. CEO compensation sensitivities and other CEO related variables
Panel A of Table 1 contains the descriptive statistics for CEO related variables. Consistent with the literature, we assume the vega of stock holdings to be zero (e.g., Coles, et al., 2006). Cash compensation is the sum of salary and bonus. All compensation variables are in millions of dollars
U
and other CEO variables (tenure and age) are in years.
N
The mean (median) vega is $167,000 ($54,000) and the mean (median) delta is $700,000
A
($246,000). The right-skewed distribution supports the observation that large bank CEOs have
M
much larger vegas and deltas than all other CEOs in the sample. These figures are broadly
D
bracketed by those obtained in other studies, despite the sample differences. In the sample of Coles
TE
et al. (2006), vega and delta (with mean of $80,000 and $600,000, respectively) are smaller, and the same is true for the medians. However, we focus on banking firms while theirs is a corporate
EP
sample ending in 2002. On the other hand, our vega and delta means are lower than those in the
CC
study by DeYoung, et al. (2013): $215,849 and $893,688, respectively. They use a smaller sample of 114 commercial banking firms over the period of 1995-2006 (573 bank-years) while we employ
A
a much broader sample of 217 banks with 1,521 bank-years. Cash compensation of $1.4 million, on the other hand, is significantly lower than the $2.5 million reported in Coles, et al. (2006), and the $2.06 million in DeYoung, et al. (2013). These figures taken in sum suggest a proclivity of banks towards stock based compensation. Mean CEO tenure is 7.75 years in our sample, close to 7 years in Coles, et al. (2006), but lower than 9.9 years in DeYoung et al. (2013). The mean and 15
median of CEO age is 57, similar to the age of 54 reported in Coles, et al. (2006). If large cash compensation, tenure, and age are indicators of entrenchment, we cannot claim that bank CEOs are more entrenched than those in nonfinancial firms.
SC RI PT
4.2.2. Risk measures We constructed the total, systematic, and unsystematic risk variables similar to Low (2009). All sample fiscal years end in December. Total risk is the natural logarithm of the annualized variance of daily returns over a year. Systematic risk is the natural logarithm of the annualized variance of
U
the predicted portion of the market model, which regresses individual stock returns on CRSP
N
value-weighted market portfolio returns, and its five lags and leads to adjust for non-synchronous
A
trading (Low, 2009). Unsystematic risk is the natural logarithm of the annualized variance of the
M
residuals of the market model. As shown in Panel B of Table 1, the mean and median values of the risk variables are close. In comparison to Low (2009), the statistics of our total risk and
D
unsystematic risk variables are broadly similar, despite a large difference in the sample.
TE
Interestingly, our log-transformed total risk mean of 6.84 is consistent with the mean of 0.017 in DeYoung et al. (2013), after applying the appropriate log-transformation to their decimal daily
EP
standard deviation without log transformation. The same consistency also holds for the median of
CC
total risk, and the mean and the median of unsystematic risk.
A
4.2.3. Firm-specific control variables Following Coles et al. (2006), we include firm size, market-to-book ratio of equity, book leverage ratio, and return on asset (ROA) as firm-specific control variables. Market capitalization, calculated as fiscal year-end stock price multiplied by the number of common shares outstanding, is the proxy for firm size. The market-to-book ratio is the ratio of market value of equity to book 16
value of equity. A higher market-to-book ratio indicates higher growth opportunities, and is expected to be positively related to firm risk. The book leverage ratio is the ratio of total debt to assets, and it relates positively to risk. ROA is presented as a percent and is defined as net income
SC RI PT
before extraordinary items and discontinued operations divided by total assets. In Panel C of Table 1, the statistics for the market-to-book ratio are similar to those in Coles et al. (2006) and DeYoung et al. (2013). Our mean (median) book leverage ratio of 0.91 (0.92) is much higher than the 0.23 (0.21) reported in Coles et al. (2006), as they excluded financial firms and utilities. However, our leverage ratio is nearly identical to the complement of the equity ratio in DeYoung, et al. (2013):
U
0.084 (0.083) for the mean (median). Typically, banks have much higher leverage ratios than
N
nonfinancial firms. Though large, our mean (median) book leverage actually indicates that our
A
banks are generally well-capitalized based on the FDIC requirements.15
M
Panel D of Table 1 presents the correlation coefficients between the various variables. The risk
D
measures are strongly correlated with one another. In addition, total and unsystematic risks are
TE
negatively correlated to the compensation structure variables (vega, delta and cash compensation), while systematic risk is positively related to them, with some cases of significance. This suggests
EP
that risk during the year is related to the compensation structure variables at the end of the year. Generally, the correlations between firm control variables, risk measures, and compensation
A
CC
sensitivities are strong and significant. 16
According to the FDIC Improvement Act in 1991, if a bank’s capital-asset ratio is above 5 percent and total riskbased ratio and Tier 1 risk-based ratio is above 10 percent and 6 percent respectively, it is well capitalized and is placed in the highest capital adequacy zone. 16 We would like to thank an anonymous referee and the editor for the suggestion to acknowledge the potential influence of outliers due to the extreme values of delta and leverage. Since winsorizing procedure will reduce our random sample, we conduct the tests with the full sample. If we winsorize the full sample only by 1 st and 99th of leverage ratio, all the results hold. If we further winsorize the full sample according to vega and delta, the results of delta become much weaker. 15
17
5. Empirical Results 5.1. Dependence of the compensation structure on past performance The presence of dynamic endogeneity is the key motivation for this study because we believe that
SC RI PT
the present compensation structure depends on the past risk-taking. Dynamic endogeneity is problematic as it causes the contemporaneous explanatory variables (vega, delta, cash compensation and even control variables) to be correlated with the lagged values of the error terms even though they are independent of the present error term. As indicated in Wintoki et al. (2012), with dynamic endogeneity, a fixed-effects regression of y on x could result in a statistically
N
U
significant coefficient for x even without a causal effect of x on y.
A
Accordingly, we test if our sample indicates the presence of dynamic endogeneity. We investigate
M
if the present compensation structure are related to past risk levels through OLS regressions of compensation variables (vega, delta and cash compensation) on lagged risk variables (total,
D
systematic and unsystematic risk). Table 2 presents the results where regressions of the levels of
TE
compensation variables are presented in Panel A, and the regressions of the changes in compensation variables are presented in Panel B. Panel A clearly shows a strong dependence of
EP
year-end compensation variables on lagged risk. In all cases, compensation structure variables –
CC
vega, delta and cash compensation – are significantly related to the risk variables in the recently completed year (at the 95 percent confidence level or better). In addition, the sign of the
A
relationship is uniformly positive with the only exception being the negative relationship between vega and systematic risk (column 2). Thus, delta, cash compensation, and vega are mostly positively associated with past levels of risk (total, systematic and unsystematic). Our results are consistent with the results of DeYoung et al. (2013) where the natural log of delta is positively 18
associated with the past level of total, systematic, and unsystematic risks in a 2SLS estimation framework. Thus, the evidence supports that the compensation structure is related to past risk levels.
SC RI PT
Panel B of Table 2 presents results of regressions similar to Panel A. However, the dependent compensation structure variables are differenced and regressed on past levels of risk and control variables. Once again, changes in delta, vega, and cash compensation are positively related to the past year’s risk levels, with traditional significances for delta and cash compensation. Therefore, boards may be responding to prior-year increases in risk levels by offering the CEO a higher delta
U
and cash compensation compared to the previous year (Berger et al., 1997; DeYoung et al., 2013;
N
Chava and Purnanandam, 2010). The relationship of the change in vega and the lagged risk is
A
positive, but significant only for the case of total risk at the 90 percent confidence level. These
M
generally uniform and strong findings in levels and first differences lend strong support to our
D
claim of dynamic endogeneity in the compensation structure.17
TE
5.2. Choosing the dynamic specification and appropriate lags for predetermined variables
EP
There are at least two reasons to conduct the tests to determine how many lags are needed in a dynamic specification (Wintoki et al., 2012).
First, the appropriate number of lags of risks to
CC
include in the model of dynamic panel GMM will insure dynamic completeness. Including too many lags will lead to overfitting, while having too few will fail to capture all past influences.
A
Therefore, including lagged risk as an explanatory variable for the current risk should help address the problem of misspecification.
17
We also ran regressions similar to Table 6 of Wintoki et al. (2012) to study the effect of risk on the future compensation. Our results, though not reported here, support the inference from Table 2. 19
While Delis and Kouretas (2011) employ one lag of risk, the literature investigating profitability of companies typically has included two lags of profitability (Gschwandtner, 2005; Wintoki et al., 2012). To decide, we run the risk measures on their four lags and control variables to determine
SC RI PT
the appropriate lag length. In the regressions with four lags of risk (columns 1, 3, and 5 of Table 3), only the first lag of risk is strongly significant for the total and unsystematic risks, and only the first two lags are strongly significant for the systematic risk, at the 99 percent confidence level. Furthermore, the model explains all three measures of risk well, with R2 measures in the vicinity of 90 percent. Therefore, using no more than two lags of risk should parsimoniously lead to
U
dynamic completeness. In the absence of the first two lags of risk, the next two lags become
N
strongly significant at mostly a 99 percent confidence level (columns 2, 4, and 6 of Table 3). The
A
R2 values remain at a comparable 85 percent or above. Therefore, the model advocates using the
M
third and fourth lags as predetermined instruments because they clearly are exogenous to the present period under the dynamic specification (i.e. with the first two lags of risk included in the
TE
D
dynamic panel for completeness).
5.3. The relationship between risk-taking and compensation structure
EP
Having established dynamic endogeneity and a dynamic specification, we now proceed to estimate
CC
the risk-compensation structure relationship as per the methodology outlined earlier. Consistent with Wintoki et al. (2012), we estimate four separate models – OLS, fixed-effects estimation,
A
dynamic OLS (DOLS) including lagged risk as controls, and dynamic GMM – to illustrate the advantages of the dynamic GMM approach by showing the differences across methodologies. OLS and dynamic OLS cannot address the bias due to unobservable heterogeneity. OLS and fixed-
20
effects estimation cannot address the dynamic relationship that the current independent variables (vega and delta) are related to the lagged dependent variable (risk). Table 4 presents the results across the four models for the three forms of risk. With the OLS model
SC RI PT
in columns 1, 5, and 9, the two risk components of unsystematic and systematic risks show mutually inconsistent relationships to vega.
Systematic risk is negatively related to vega
(significant at 99 percent), while unsystematic risk is positively related to vega with a marginal significance.
As a result, total risk has a small and insignificant coefficient on vega. The
relationship with delta demonstrates remarkable consistency, though. The three types of risk
U
positively relate to delta, with significances at 99 percent for total and unsystematic risks. Cash
N
compensation is positively related to the three forms of risk at 90 percent or better. However,
A
unobservable firm-level heterogeneity casts doubt over these results, and we next present fixed-
M
effects regressions to remove firm level heterogeneity.18
D
Estimation results of fixed-effects models are presented in columns 2, 6, and 10 of Table 4.
TE
Wintoki et al. (2012) presents an important critique of fixed-effects regressions in a dynamic context. They hypothesize and empirically show that the fixed-effects regression of y on x will be
EP
negatively (positively) biased if x is positively (negatively) related to lagged y values (See Eq. 5,
CC
and Tables 6 and 7 of their paper). 19 Our context is also dynamic, and we find a very similar result. As shown in Panel A of Table 2, we found that vega, delta, and cash compensation
A
positively relate to the three forms of lagged risk, barring the only exception of vega and systematic
18
Financial institutions have their own unique culture and CEOs differ in managerial ability and aggressiveness. As an example, aggressive CEOs or institutions may engage in substantial unsystematic risk-taking despite low vegas. 19 Wintoki et al. (2012) analytically show that fixed-effects estimation coefficients of performance-governance relation will be negatively biased if governance variables are positively related to lagged value of performance variables (i.e., a dynamic model), and provide empirical support for this hypotheses through their Table 6. 21
risk (column 2). In columns 2, 6 and 10 of Table 4, all nine fixed-effects estimation coefficients (three types of risk and three compensation variables) except one (coefficient of delta in column 10) are negative. Therefore, we conclude that the obtained fixed-effects coefficients are negatively
SC RI PT
biased as the methodology ignores the dynamic relationship between risk and compensation variables. However, removal of firm-level heterogeneity through firm dummies clearly yields a better fit as the R2 is higher by at least seven percent compared to OLS regressions. The fixedeffects estimation underscores the need for a dynamic panel GMM that can admit firm fixedeffects, while addressing dynamic endogeneity.
U
Next, we include two lags of risk and perform dynamic OLS estimation (columns 3, 7 and 11 of
N
Table 4). Note that there is no correction for endogeneity yet. One lag of risk is a strong predictor
A
of the current values of the three types of risk, as the coefficient at the first lag is positive and
M
significant at the 99 percent confidence level. The R2 is higher by at least seven percent, once again
D
compared to the OLS regressions. Vega is now unrelated to unsystematic and total risks, but
TE
negatively related to systematic risk with a marginal significance at 90 percent. For delta, the result is more interesting for unsystematic and total risks: delta appears to encourage unsystematic
EP
risk taking, which also increases total risk. Cash compensation does not appear to affect risk taking in any of the three forms of risk. Even without a correction for endogeneity, dynamic OLS suggest
CC
that vega and cash compensation do not appear to be related to risk-taking, but delta does.
A
With the dynamic panel GMM estimation to correct for endogeneity, we see a strong consistency between risk and vega in columns 4, 8 and 12 of Table 4. The coefficient on vega is always positive but marginally significant at 90 per cent only in the case of unsystematic risk (column 12). Thus, the null hypothesis of no risk-vega relationship cannot be rejected. This result is consistent 22
with that of Fahlenbrach and Stulz (2011) indicating that risk aversion of bank CEO, regulatory supervision and monitoring by bondholders mitigate the risk-taking incentives from vega. As explained in Fahlenbrach and Stulz (2011), given most of the CEO’s option holdings are in-the-
SC RI PT
money, the risk incentive from option compensation (vega) is similar to that from stock compensation and the CEO becomes more conservative (Ross, 2004; Carpenter, 2000).
For the risk-delta relationship, there is consistent and strong evidence across the board with the dynamic GMM model. In columns 4, 8 and 12 of Table 4, delta increases all three risks at 99 percent confidence levels, leading us to reject our null hypothesis of no relationship. The
U
significant positive relationship between bank risk and delta suggests that large stock grants in the
N
banking industry align the interest of a CEO with that of shareholders to improve the long-term
A
performance of the bank. This increased risk taking in delta found in our study is contrary to
M
DeYoung et al. (2013) who document a risk-inhibiting effect of delta using 2SLS with a
D
commercial bank sample, but it is consistent with several other studies with both financial and
TE
nonfinancial samples (Fahlenbrach and Stulz, 2011; Armstrong and Vashishtha, 2012; Coles et al., 2006). For example, Fahlenbrach and Stulz (2011) show that firms with high-delta CEOs
EP
performed worse during the crisis years, implying a positive risk-delta relationship. Our results are also consistent with Armstrong and Vashistha (2012) and Coles et al. (2006) in terms of the sign
CC
and significance of the coefficient of delta, though they use delta as a control variable and their
A
sample is nonfinancial firms. Our results support the argument of Saunders et al. (1990) that, as long as managerial ownership is not too high to make managers very sensitive to the undiversifiable risk of human capital, CEOs in shareholder-controlled banks, which align the
23
incentives of the managers with those of the shareholders through stocks and stock options, take higher risk. 20 In Columns 4, 8 and 12 of Table 4, cash compensation carries negative signs for all three measures
SC RI PT
of risk but the significances are consistently marginal (at the 90 percent level), providing weak evidence against the null hypothesis of no relationship. These general negative coefficients may support the argument by Berger et al.(1997) that higher cash compensation makes bank CEOs more conservative. Empirically our results on cash compensation are consistent in sign with those reported in Armstrong and Vashishtha (2012) and Coles et al. (2006), suggesting that higher cash
U
compensation leads CEOs to avoid risk to protect their human capital. We separated cash
A
M
coefficient on bonus remained insignificant.
N
compensation into salary and bonus, as bonus can be a risk-increasing device. However, the
The economic significances of the coefficients in columns 4, 8 and 12 are modest as well. A one
D
standard deviation increase of vega (0.314 million dollars) is associated with 0.10 standard
TE
deviation increase of unsystematic risk.21 One standard deviation of delta (2.203 million dollars) increases total, systematic, and unsystematic risks by 0.07, 0.05, and 0.08 standard deviation of
A
CC
EP
these three risks respectively.22 For cash compensation, a one standard deviation decrease of cash
20
Though ex-post in nature and not presented here, we also checked our sample to find bank holding companies (BHC) where at least a subsidiary failed during the financial crisis. Our sample contains only seven BHCs with failed subsidiaries that account for 46 observations. Removing these observations leaves the estimates largely unchanged. 21 Unsystematic risk increases by 0.097654 (=0.311*0.314). The standard deviation of unsystematic risk is 0.956 and this increase is equal to 0.10 standard deviation (0.097654/0.956=0.102). 22 Total risk increases by 0.07 standard deviation (2.203*0.029 = 0.063887; 0.063887/0.971=0.066), systematic risk increases by 0.050 standard deviation (2.203*0.028=0.061684; 0.061684/1.245=0.049545), and unsystematic risk increases by 0.076 standard deviation (2.203*0.033=0.072699; 0.072699/0.956=0.076). 24
compensation (1.448 million dollars) is related to 0.14, 0.16, and 0.15 standard deviation increases of these three risks respectively.23 In the specification tests presented at the bottom of Table 4, the p-values of the AR(2) tests are at
SC RI PT
least 0.25 across all three forms of risk. Therefore, the null hypothesis of no second-order serial correlation cannot be rejected. This satisfies the Arellano and Bond (1991) requirement of no serial correlation beyond one lag, and justifies the use of the predetermined variables as instruments. Hansen’s J-statistic, that tests overidentifying restrictions, has relatively large pvalues of higher than 18 percent for all three forms of risks. Therefore, the null hypothesis that
N
U
our instruments are valid cannot be rejected.
A
As explained in model specification in Section 3, we include the level equation in the system GMM
M
estimation following Arellano and Bover (1995) and Blundell and Bond (1998). The introduction of the level equation adds new instruments in the model, and we need to ensure that this subset of
D
instruments is also exogenous. Here, Difference-in-Hansen test of exogeneity provides further
TE
support, as the p-values are uniformly in excess of 0.27. Therefore, the exogeneity of additional instruments, our null hypothesis, cannot be rejected. This assures that the introduction of the level
EP
equation in the system GMM does not adversely affect the estimation.
CC
Before advancing to the next section, we address the concern if the results of Table 4 are driven by the outliers of vega, and delta. Large banks provide their CEOs with compensations that are
A
significantly higher than the typical bank CEO compensation. This pattern for delta and vega is evident in Table 1 as the gap between quartiles is enormous for the top quartile (75 percentile to
23
Total, systematic and unsystematic risks decrease by 0.14 standard deviation (-95.626*1.448/1000= -0.138466; 0.138466/0.971= -0.1426), 0.16 standard deviation (-138.130*1.448/1000= -0.2; -0.2/1.245=-0.1606), and 0.15 standard deviation (-96.319*1.448/1000 = -0.13947; -0.13947/0.956= -0.14589), respectively. 25
maximum), relative to the other quartiles. We address this concern in two different ways. First, we delete all observations for banks with assets greater than $100 billion (156 observations). The resulting GMM estimation, not presented here but available from the authors, provides
SC RI PT
substantially the same results as in Table 4. Vega is unrelated to all three forms of risk, while delta is positively related to all three forms of risk with significances of at least 95 percent confidence level. Next, we compute vega and delta as percentages of total compensation and re-estimate Table 4. Our results largely stand as total risk and unsystematic risk are still significantly and positively dependent on delta (though the delta coefficient for systematic risk is now negative but
N
while it is significantly negative for systematic risk.
U
insignificant). Likewise, the coefficient on vega is insignificant for total and unsystematic risks,
M
A
6. The influence of the commercial bank sample, bank size and leverage Our primary result is that bank risk is positively related to delta but unrelated to vega. However,
D
the result could be affected by bank characteristics such as different types of depository
TE
institutions, bank size, and bank leverage. First, with a sample of commercial banks, DeYoung et al. (2013) study the bank risk-vega relationship and document that vega encourages risk-taking,
EP
while delta curbs it. We instead find a contrary result with our comprehensive sample including
CC
commercial banks, federally chartered savings institutions (SIC code = 6035) and state-chartered savings institutions (SIC code = 6036). Second, large banks are different from small banks in terms
A
of business model: large banks engage more in risky nontraditional banking businesses (investment banking, security brokerage, and securitization), while small banks generally rely on the traditional “originate-to-hold” lending model and control their credit risk by intensive monitoring and maintaining long-term lending relationships with their customers (DeYoung and 26
Torna, 2013). It is possible that CEOs in large and small banks have different compensation incentive mechanisms, which might drive our primary result. Third, excessive bank leverage has always been an issue of concern, and the Basel III accord and the recent bank regulation seek to
SC RI PT
encourage banks to carry more equity to control risk-taking. Therefore, we now incorporate three key bank characteristics into our tests.
We explore if different types of depository institutions, bank size and leverage affect the positive risk-vega relationship through the use of dummy variables. We assign the dummy variable SIC6020 a value of one for commercial banks. Otherwise, the variable is assigned a value of zero
U
(savings institutions). Second, we define a bank size dummy by its capitalization. We annually
N
rank banks in order of size at the beginning of the calendar year, and assign the top half to large
A
banks. The indicator variable LARGE equals one for large banks (zero otherwise). A third dummy
M
variable (HIGHLEV) is defined as one if the bank has a higher leverage ratio than the sample
D
median value in each year (zero otherwise).
TE
We include the interactions of the three dummy variables with vega and delta into the dynamic GMM model, and the estimation results are reported in Table 5.
First, vega is no longer
EP
significantly related to risk in its three forms (unsystematic, systematic, and total), even at the 90
CC
percent confidence level. In Table 4, it was marginally positively related to the unsystematic risk. The coefficient of the interaction term between leverage and vega (Vegat-1*HIGHLEV) is positive
A
for the three forms of risk, but only significant for systematic risk at the 95 percent confidence level. This indicates that, for high leverage institutions, CEO compensation vega appears to positively increase systematic risk. Regulators should pay close attention to option grants in banks with inadequate capital since the associated high pay-risk sensitivity (vega) may lead to excessive 27
systematic risk-taking. The results of the vega interaction of the other two characteristics (SIC6020 and LARGE) are uniformly insignificant. Further, the positive risk-delta relation, previously obtained in Table 4, is significantly weakened
SC RI PT
after the inclusion of the three indicator variables, though the coefficient of delta by itself is still positive and marginally significant at the 90 percent confidence level in the model of systematic risk in Table 5. This is consistent with our primary result in Table 4, which indicates that a greater sensitivity of the CEO’s wealth to stock price (larger delta) motivates the CEO to take higher systematic risk to improve bank performance and associated CEO wealth for the entire sample.
U
Interestingly, interactions of delta with SIC6020 and HIGHLEV carry negative signs across all
N
three risk models indicating that commercial bank and high-leverage bank CEOs demonstrate a
A
reduced incentive for risk-taking in delta. The coefficients of the interaction terms between
M
SIC6020 and delta for systematic and unsystematic risks are significant at the 95 percent
D
confidence level, though total risk only has marginal significance at the 90 percent confidence
TE
level, indicating that commercial banks reduce risk-taking in delta compared to savings institutions. This result is consistent with that of DeYoung et al. (2013) who found that delta is
EP
negatively related to risk-taking in the commercial bank sample.
CC
The coefficients of the interaction terms between the leverage indicator variable and delta (deltat1*HIGHLEV)
are all negative. Here the interaction of delta with HIGHLEV is only marginally
A
significant at the 90 percent confidence level for systematic risk, and at the 95 percent confidence level for unsystematic risk. Therefore, compensation delta discourages risk-taking for highleverage firms. So, why do low-leverage bank CEOs take risk in compensation delta, but not the high-leverage bank CEOs? According to Fahlenbrach and Stulz (2011), a higher delta (sensitivity 28
of a CEO’s wealth to stock price) motivates the CEO to improve her bank’s long-term performance, which is reflected on stock price. Empirical evidence generally supports that lower leverage level (higher capital ratio) is associated with better bank performance (see buy-and-hold
SC RI PT
returns in Fahlenbrach and Stulz (2011) and survival and market share in Berger and Bouwman (2013)). Therefore, it is very likely that the low-leverage bank CEO takes risk in delta to enhance long-term bank performance, whereas the high-leverage bank CEO becomes more conservative and reduces risk-taking in delta to mitigate the detrimental effect of high leverage on bank performance. Furthermore, as noted earlier, academic theory offers several compelling reasons.
U
First, bondholders may aggressively monitor high-leverage banks which may reduce risk-taking
N
in compensation delta (e.g., John and Qian, 2003; John et al., 2010). Second, at high leverage
A
levels, rating agencies may be more sensitive to the CEO’s compensation delta and the CEO starts
M
to curb risk-taking. In addition, aggressive supervision of high leverage banks might make risktaking incentives less important or irrelevant (e.g., Booth et al., 2002). 24 In terms of model
EP
7. Conclusion
TE
specified model.
D
specification, the robustness statistics for the dynamic panel GMM estimation indicate a well-
CC
Convexity of the compensation package motivates CEOs to accept risky positive-NPV projects that they might otherwise forego. Using different samples of firms excluding financial institutions
A
and utilities, prominent studies find strong empirical support for the foregoing assertion. Nevertheless, convincing arguments exist that financial institutions, due to regulatory supervision
24
However, we need to be also aware that high leverage in the banking industry may motivate a CEO to take excessive risk in delta, because payoffs to the equity holder of a levered firm resemble those of a call option. This is due to the risk-shifting incentive to the equity holder to take advantage of the debtholder (Ross et al., 2010; Harris and Raviv, 1991). 29
and high leverage, might have a weaker or non-existent risk-vega relationship. Also, Carpenter (2000), Ross (2004), and Lewellen (2006), among others, model a risk-averse CEO and challenge the above assertion by showing that the risk-vega relationship may not always be positive. Finally,
SC RI PT
empirical evidence of early exercise, motivated by moneyness and vesting, strongly supports the view of a risk-averse CEO (Huddart and Lang, 1996; Hemmer et al., 1996; Heath, et al., 1999; Hall and Murphy, 2002; Bettis et al., 2005).
Our dynamic panel GMM estimator finds significant evidence that, for financial institutions in aggregate, risk increases in compensation delta, but not in vega. This result is similar to the crisis-
U
period analysis of Fahlenbrach and Stulz (2011). Our results differ from DeYoung et al. (2013)
N
who find vega to be risk increasing and delta to be risk moderating. However, institutional
M
A
CC
EP
TE
D
delta, unlike the aggregate result.
A
characteristics matter. Commercial banks and high leverage institutions tend to reduce risk in
30
Reference
SC RI PT
Amadeus, M., Sadka, R.(2015). Executive compensation convexity and firm crash risk. Available at SSRN: https://ssrn.com/abstract=2625852 or http://dx.doi.org/10.2139/ssrn.2625852 Anantharaman, D., Lee, Y.G.(2014). Managerial risk taking incentives and corporate pension policy. Journal of Financial Economics, 111(2), 328-351. Arellano, M., Bover, O.(1995). Another look at the instrumental variable estimation of errorcomponent models. Journal of Econometrics, 68, 29–51.
U
Arellano, M., Bond, S.(1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations, Review of Economic Studies, 58 (2), 277-297.
N
Armstrong, C.S., Vashishtha, R.(2012). Executive stock options, differential risk-taking incentives, and firm value, Journal of Financial Economics, 104(1), 70-88.
M
A
Bai, G., Elyasiani, E. (2013). Bank stability and managerial compensation. Journal of Banking & Finance 37, 799-813.
D
Berger, A, Imbierowicz, B., Rauch, C. (2016). The roles of corporate governance in bank failures during the recent financial crisis. Journal of Money, Credit and Banking, 48, 729–770.
TE
Berger, A. N., Bouwman, C. H.S.(2013). How does capital affect bank performance during financial crises? Journal of Financial Economics 109, 146-176.
EP
Berger, P., Ofek, E., Yermack, D.(1997). Managerial entrenchment and capital structure decisions. Journal of Finance 52, 1411-1438.
CC
Bettis J. C., Bizjak, J. M., Lemmon, M. L.(2005). Exercise behavior, valuation, and the incentive effects of employee stock options, Journal of Financial Economics, 76(2), 445-470.
A
Black, F., Scholes, M.(1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654. Blundell, R., Bond, S.(1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87, 115–143. Booth, J. R., Cornett, M. M., Tehranian, H.(2002). Boards of directors, ownership, and regulation. Journal of Banking and Finance, 26, 1973-1996.
31
Carpenter, J. (2000). Does option compensation increase managerial risk appetite? The Journal of Finance, 55(5), 2311-2331. Chava, S., Purnanandam, A.(2010). CEOs versus CFOs: Incentives and corporate policies. Journal of Financial Economics, 97(2), 263-278.
SC RI PT
Coles, J.L., Daniel, N.D., Naveen, L.(2006). Managerial incentives and risk-taking. Journal of Financial Economics, 79, 431-468. Core, J., Guay, W.(1999). The use of equity grants to manage optimal equity incentive levels. Journal of Accounting and Economics, 28, 151-84.
Core J., Guay, W.R.(2002). Estimating the value of executive stock option portfolios and their sensitivities to price and volatility. Journal of Accounting Research, 40, 613–630.
U
Crawford, A. J., Ezzell, J. R., & Miles, J. A.(1995). Bank CEO pay-performance relations and the effects of deregulation. Journal of Business, 68(2), 231-256.
A
N
Delis, M.D., Kouretas, G.P.(2011). Interest rates and bank risk-taking. Journal of Banking &Finance, 35(4), 840-855.
M
DeYoung, R., Peng, E., Yan, M.(2013). Executive compensation and business policy choices at U.S. commercial banks. Journal of Financial and Quantitative Analysis, 48(1), 165-196.
D
DeYoung, R., Torna, G.(2013). Nontraditional banking activities and bank failures during the financial crisis. Journal of Financial Intermediation 22, 397-421.
TE
Ellul, A. and Yerramilli, V. (2013). Stronger Risk Controls, Lower Risk: Evidence from U.S. Bank Holding Companies. The Journal of Finance, 68, 1757-1803.
EP
Fahlenbrach, R., Stulz, R.(2011). Bank CEO incentives and the credit crisis. Journal of Financial Economics, 99, 11-26.
CC
Fiordelisi, F., Marques-Ibanez, D., Molyneux, P.(2011). Efficiency and risk in European banking. Journal of Banking and Finance, 35(5), 1315-1326.
A
Gschwandtner, A.(2005). Profit persistence in the ‘very’ long run: evidence from survivors and exiters. Applied Economics 37, 793–806. Guay, W.R. (1999). The sensitivity of CEO wealth to equity risk: An analysis of the magnitude and determinants. Journal of Financial Economics, 53, 43–71. Hagendorff, J., Vallascas, F. (2011). CEO pay incentives and risk-taking: Evidence from bank acquisitions. Journal of Corporate Finance, 17(4), 1078-1095. 32
Hall, B.J., Murphy, K.J. (2002). Stock options for undiversified executives. Journal of Accounting and Economics, 33, 3–42. Harris, M., Raviv, A. (1991). The theory of capital structure. Journal of Finance 46:297–355. Hayes, R. M., Lemmon, M., Qiu M. (2012). Stock options and managerial incentives for risk taking: Evidence from FAS 123R. Journal of Financial Economics, 105, 174-190.
SC RI PT
Heath, C., Huddart, S., Lang, M.(1999). Psychological factors and stock option exercise, Quarterly Journal of Economics, 114, 601-628.
Hemmer, T., Matsunaga, S., Shevlin, T.(1996). The influence of risk diversification on the early exercise of employee stock options by executive officers. Journal of Accounting and Economics, 21(1), 45-68.
U
Hermalin, B.E., Weisbach M.S.(1991). The effects of board composition and direct incentives on firm performance. Financial Management, 20(4), 101-112.
A
N
Himmelberg, C., Hubbard, R.G., Palia, D.(1999). Understanding the determinants of managerial ownership and the link between ownership and performance, Journal of Financial Economics, 53(3), 353-384.
M
Hubbard, R.G., Palia, D.(1995). Executive pay and performance evidence form the U.S. banking industry. Journal of Financial Economics, 39, 105-130.
D
Huddart S., Lang M. (1996). Employee stock option exercises an empirical analysis. Journal of Accounting and Economics, 21(1), 5-43.
TE
Jensen, M.C., Meckling, W.H.(1976). Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3, 305-360.
EP
John, T.A., John, K.(1993). Top-management compensation and capital structure. Journal of Finance, 48, 949-974.
CC
John K., Saunders, A., Senbet, L.W. (2000). A theory of bank regulation and management compensation. Review of Financial Studies, 13, 95-125.
A
John, K., Qian, Y.(2003). Incentive features in CEO compensation in the banking industry. Federal Reserve Bank of New York Economic Policy Review 9, 109–121. John, K., Mehran, H., Qian, Y.(2010). Outside monitoring and CEO compensation in the banking industry. Journal of Corporate Finance. 16, 383-399.
33
Koutsomanoli-Filippaki, A. Mamatzakis, E.(2009). Performance and Merton-type default risk of listed banks in the EU: A panel VAR approach. Journal of Banking and Finance, 33 (11). 20502061. Lambert, R. A., Larcker, D. F., Verrecchia, R. E.(1991). Portfolio considerations in valuing executive compensation. Journal of Accounting Research, 29, 129-49.
SC RI PT
Lewellen, K.(2006). Financing decisions when managers are risk averse. Journal of Financial Economics, 82, 551-589. Low, A.(2009). Managerial risk-taking behavior and equity-based compensation. Journal of Financial Economics, 92, 470-490. Pathan, S.(2009). Strong boards, CEO power and bank risk-taking. Journal of Banking and Finance, 33(7), 1340-1350.
N
U
Parrino, R., Poteshman, A. M., Weisbach, M. S.(2005). Measuring investment distortions when risk-averse managers decide whether to undertake risky projects. Financial Management, 34(1), 21-50.
M
A
Rajgopal, S., Shevlin, T.(2002).Empirical evidence on the relation between stock option compensation and risk taking, Journal of Accounting and Economics, 33(2), 145-171. Ross, S.A., Westerfield, R.W., Jaffee, J. (2010). Corporate Finance, 9th edition, McGraw-Hill.
D
Ross, S.A.(2004). Compensation, incentives, and the duality of risk aversion and riskiness. Journal of Finance, 59, 207–225.
TE
Wintoki, M.B., Linck, J. S., Netter, J. M.(2012). Endogeneity and the dynamics of internal corporate governance? Journal of Financial Economics, 105, 581-606.
A
CC
EP
Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics 126: 25-51.
34
Table 1：Descriptive Statistics of the Sample
SC RI PT
Categorized summary statistics for the variables from the 1993-2009 period are presented in Panels A through D. Panel A contains CEO related variables – compensation sensitivities (delta and vega) and their constituents, cash compensation (salary plus bonus), tenure (years of service as the CEO) and CEO’s age. All compensation structure variables are in millions of dollars. Deltas and vegas are computed with the one-year approximation method of Core and Guay (2002). Panel B contains the firm risk measures – total, systematic, and and unsystematic risks. The risk measures are computed using daily data over the fiscal year are presented as natural logs annualized variances. Similar to Low (2009), five leads and five lags of CRSP value-weighted portfolio returns are included in the market model regression to account for nonsynchronous trading. This regression is used to decompose total risk into unsystematic and systematic components. Panel C presents other firm specific control variables. Market capitalization is the natural log of the fiscal year end stock price multiplied by the company's common shares outstanding. Market to book ratio is the ratio of market value of equity to book value of equity. Book leverage ratio (in decimal) and ROA (in percent) are, respectively, total debt and net income before extraordinary items and discontinued operations, divided by total assets. Panel D presents the correlation matrix of all variables and pvalues are below the correlation coefficients.
Panel A: CEO related variables
0 0
0.020
0.054
0.168
3.816
0
0.655
0.965
1.533
15.500
3.000
6.000
11.000
42.000
53.000
57.000
61.000
80.000
Std. Dev. 2.203
Vega ($millions) Cash Compensation (Salary + Bonus, $millions)
1521
0.167
0.314
1521
1.403
1.448
CEO tenure (years)
1521
7.745
6.565
0
CEO age (years)
1521
56.959
32
Total Risk
1521
Panel B: Risk Measures 6.840 0.971 4.658
Systematic risk
1521
Unsystematic risk
1521
Market capitalization
N
6.168
6.685
7.283
11.334
1.245
2.138
4.755
5.448
6.215
9.194
6.393
0.956
4.299
5.753
6.248
6.897
11.245
Panel C: Other Firm Control Variables 1521 8025.90 19487.97 19.146 866.53 0 0 8 1521 2.123 1.133 -0.463 1.430
1958.07 0 1.919
6138.21 0 2.585
239757.83 14.3640
1521
0.913
0.031
0.556
0.903
0.918
0.929
1.012
1521
0.976
1.064
-16.195
0.844
1.122
1.374
4.315
A
CC
EP
ROA
Max 40.740
5.589
TE
Book leverage ratio
75th 0.627
A
6.372
D
Market to book ratio
Min
U
Mean 0.700
Delta ($millions)
Percentile 50th 0.246
25th 0.096
N 1521
M
Variable
35
N U SC RI PT
Panel D: Correlation Matrix of Sensitivities, Risk Measures and Control Variables
Total risk Systematic risk
0.864 <.0001 1
Unsystematic risk
Unsystematic. risk 0.960 <.0001 0.704 <.0001 1
Vega
Cash compensation
Age
-0.021 0.4233 0.017 0.5142 -0.032 0.2174 0.272 <.0001 1
-0.116 <.0001 0.011 0.6733 -0.170 <.0001 0.563 <.0001 0.291 <.0001 1
A
CC E
PT
Log(Market Cap)
Book Leverage
-0.068 0.0083 0.077 0.0027 -0.149 <.0001 1
Cash Compensation
ED
Tenure
Market to Book ratio
Delta
M
Delta
Vega
A
Systematic risk
36
Tenure
Age
0.027 0.2844 0.055 0.0334 0.016 0.5231 -0.046 0.0713 0.196 <.0001 -0.056 0.0282 1
-0.021 0.4025 -0.010 0.7078 -0.017 0.5069 0.042 0.1003 0.182 <.0001 0.075 0.0034 0.396 <.0001 1
Market capitalization -0.246 <.0001 -0.015 0.552 -0.335 <.0001 0.635 <.0001 0.281 <.0001 0.612 <.0001 -0.044 0.0846 0.037 0.1534 1
Market to book -0.163 <.0001 -0.108 <.0001 -0.164 <.0001 0.115 <.0001 0.234 <.0001 0.215 <.0001 -0.056 0.0291 -0.116 <.0001 0.284 <.0001 1
Book Leverage 0.092 0.0004 0.016 0.5285 0.128 <.0001 0.008 0.7657 -0.056 0.0299 0.075 0.0033 -0.014 0.5868 -0.083 0.0012 -0.002 0.9236 0.097 0.0001 1
ROA -0.499 <.0001 -0.399 <.0001 -0.508 <.0001 0.130 <.0001 0.173 <.0001 0.157 <.0001 -0.025 0.3228 -0.011 0.6594 0.308 <.0001 0.428 <.0001 -0.222 <.0001
N U SC RI PT
Table 2: Relationship between compensation variables and past risk variables
The table presents OLS regression of compensation structure on past risk as well as control variables. Panel A contains a regression of the compensation structure levels while Panel B contains a regression of the change in compensation structure variables on lagged risk and control variables. The columns represent the compensation variables (vega, delta, and cash compensation), and the three measures of risk. Control variables are CEO tenure, age, logarithm of market capitalization, market to book ratio, book value of leverage, and ROA. The risk variables (total, systematic and unsystematic) and control variables are one year lagged values. Year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively.
(1) 0.041*** (2.98)
Systematic riskt-1
-0.026** (-2.44)
Aget-1 Log(Market Cap)t-1
CC E
Market to Book ratiot-1 Book Leveraget-1 ROAt-1
A
Constant
-0.003** (-2.53) 0.002* (1.76) 0.145*** (31.53) -0.012* (-1.69) 0.440** (2.04) -0.000 (-0.00) -1.799*** (-7.99) Yes 1,521 0.466
Year Dummies Observations R-squared
-0.003*** (-2.94) 0.002** (2.11) 0.144*** (31.66) -0.007 (-1.08) 0.595*** (2.75) -0.009 (-1.19) -1.556*** (-7.28) Yes 1,521 0.465
PT
Tenuret-1
ED
Unsystematic riskt-1
Panel A: Dependent variable is level at time t Deltat (3) (4) (5) (6) 0.587*** (4.97) 0.206** (2.21) 0.042*** 0.585*** (3.34) (5.45) -0.003** 0.060*** 0.058*** 0.059*** (-2.56) (6.86) (6.58) (6.83) 0.002* 0.042*** 0.043*** 0.042*** (1.75) (4.65) (4.78) (4.65) 0.147*** 0.396*** 0.334*** 0.431*** (30.81) (9.97) (8.47) (10.41) -0.012* 0.387*** 0.408*** 0.388*** (-1.69) (6.46) (6.77) (6.49) 0.455** -5.417*** -4.921*** -5.179*** (2.12) (-2.91) (-2.62) (-2.80) 0.002 0.133** 0.070 0.153** (0.20) (2.00) (1.08) (2.28) -1.829*** -5.110*** -2.266 -5.469*** (-8.12) (-2.63) (-1.22) (-2.81) Yes Yes Yes Yes 1,521 1,521 1,521 1,521 0.467 0.190 0.180 0.193
A
Total riskt-1
Vegat (2)
(7) 0.406*** (6.24)
37
Cash compensationt (8)
(9)
0.284*** (5.55)
M
VARIABLES
-0.010** (-2.02) 0.017*** (3.50) 0.630*** (28.76) 0.042 (1.26) 1.806* (1.76) -0.045 (-1.24) -8.773*** (-8.18) Yes 1,521 0.431
-0.010** (-2.12) 0.017*** (3.51) 0.577*** (26.65) 0.046 (1.40) 1.724* (1.67) -0.073** (-2.03) -6.965*** (-6.82) Yes 1,521 0.428
0.277*** (4.65) -0.011** (-2.21) 0.018*** (3.59) 0.636*** (27.71) 0.050 (1.50) 2.162** (2.10) -0.055 (-1.48) -8.272*** (-7.65) Yes 1,521 0.424
Systematic risk t-1 Unsystematic risk t-1
Log(MV) t-1 Market to Book ratio t-1 Book Leverage t-1 ROA t-1
CC E
Constant
ED
Age t-1
-0.000 (-0.62) -0.001 (-1.21) 0.012*** (3.23) 0.010** (2.02) -0.186 (-1.11) -0.004 (-0.53) 0.029 (0.17) Yes 1,274 0.071
PT
Tenure t-1
A
Year Dummies Observations R-squared
N U SC RI PT
(1) 0.020* (1.81)
A
Total risk t-1
Panel B: Dependent variable is change from t to t-1 Vega) t Delta) t (2) (3) (4) (5) (6) 0.189*** (4.64) 0.007 0.156*** (0.86) (5.09) 0.011 0.152*** (1.08) (4.00) 0.000 -0.001 0.004 0.004 0.004 (0.28) (-0.70) (1.40) (1.46) (1.25) 0.001 -0.001 0.003 0.003 0.003 (0.82) (-1.16) (1.02) (0.92) (1.10) 0.009** 0.012*** 0.029** 0.001 0.034** (2.49) (3.01) (2.11) (0.08) (2.40) 0.013** 0.011** 0.087*** 0.086*** 0.090*** (2.43) (2.14) (4.50) (4.49) (4.65) -0.020 -0.169 -1.123* -1.272** -0.997 (-0.11) (-1.01) (-1.80) (-2.04) (-1.60) 0.000 -0.004 0.064*** 0.058** 0.064*** (0.03) (-0.62) (2.60) (2.37) (2.59) -0.128 -0.019 -0.462 0.311 -0.718 (-0.73) (-0.11) (-0.71) (0.51) (-1.11) Yes Yes Yes Yes Yes 1,274 1,274 1,274 1,274 1,274 0.069 0.070 0.121 0.124 0.117
M
VARIABLES
38
Cash compensation) t (7) (8) (9)
0.156** (2.43) 0.164*** (3.41)
-0.003 (-0.66) -0.003 (-0.70) -0.016 (-0.76) -0.008 (-0.27) -0.048 (-0.05) -0.034 (-0.87) -0.235 (-0.23)
-0.003 (-0.56) -0.004 (-0.81) -0.041** (-2.00) -0.011 (-0.38) -0.261 (-0.27) -0.036 (-0.94) 0.354 (0.37)
0.114* (1.92) -0.003 (-0.74) -0.003 (-0.65) -0.013 (-0.59) -0.005 (-0.17) 0.064 (0.07) -0.035 (-0.89) -1.225 (-1.21)
Yes 1,274 0.086
Yes 1,274 0.091
Yes 1,274 0.085
N U SC RI PT
Table 3: Risk persistence over time
The table presents OLS regression of risk levels on past risk levels, as well as control variables to establish risk persistence. The columns represent the risk variables (total, systematic and unsystematic). Control variables are CEO tenure, age, logarithm of market capitalization, market to book ratio, book value of leverage, and ROA. Year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively. Total Risk t VARIABLES risk t-1
M
risk t-3
Age t
PT
Log(MV) t
ED
risk t-4 Tenure t
CC E
Market to Book ratio t Book Leverage t
A
ROA t
Intercept
Year Dummies Observations R-squared
(2)
A
risk t-2
(1) 0.622*** (15.73) 0.063 (1.35) 0.016 (0.34) -0.020 (-0.48) 0.000 (0.25) -0.001 (-0.42) 0.001 (0.13) 0.020 (1.29) 1.825*** (3.24) -0.137*** (-8.63) 0.275 (0.47) Yes 716 0.923
Systematic Risk t (3) (4) 0.453*** (12.65) 0.122*** (3.34) 0.007 0.206*** (0.20) (5.82) -0.003 0.099*** (-0.08) (2.83) -0.001 -0.005* (-0.33) (-1.73) -0.003 -0.001 (-1.01) (-0.31) 0.019* 0.013 (1.69) (1.03) 0.039** 0.073*** (2.14) (3.51) 0.862 0.318 (1.27) (0.42) -0.101*** -0.135*** (-5.44) (-6.30) 1.103* 3.461*** (1.70) (4.71) Yes Yes 716 748 0.904 0.864
0.293*** (6.00) 0.106** (2.20) -0.001 (-0.61) -0.001 (-0.21) -0.008 (-0.67) 0.049*** (2.65) 1.010 (1.51) -0.205*** (-10.79) 5.579*** (8.18) Yes 748 0.877
39
Unsystematic Risk t (5) (6) 0.596*** (14.48) 0.060 (1.22) 0.080* 0.333*** (1.66) (6.58) -0.020 0.120** (-0.47) (2.42) 0.002 0.001 (0.82) (0.30) -0.000 -0.001 (-0.08) (-0.45) -0.005 -0.024* (-0.45) (-1.77) 0.014 0.042** (0.78) (2.04) 1.958*** 0.895 (2.98) (1.19) -0.168*** -0.251*** (-9.01) (-11.70) -0.144 2.030** (-0.21) (2.52) Yes Yes 716 748 0.898 0.848
N U SC RI PT
Table 4: The relationship between risk and lagged values of compensation variables for all banks (SIC Code = 6020, 6035, and 6036) This table reports the dynamic panel GMM estimation of the model, along with other models, as follows:
Risk i ,t 0 1 Risk i ,t 1 2 Risk i ,t 2 1Vega i ,t 1 2 Delta i ,t 1 3 CashCompensation i ,t 1 ControlVar aibles i ,t YearDummies i i ,t
Total Risk t
(-8.76) 0.053***
(-4.96) 0.010
(-1.13) 0.012
(-0.14) -0.030
(4.72) 0.062***
(-0.60) 0.016
(3.24) 0.030**
(2.64) -0.009
(-12.84) 0.049***
(-6.08) 0.004
(-2.80) 0.004
(-0.92) -0.035
Leverage t
(3.92) 1.932***
(0.57) -1.178
(1.00) 1.717***
(-1.01) 2.470***
(3.63) 2.742***
(0.73) -0.216
(1.97) 1.561***
(-0.25) 2.791**
(3.29) 1.701***
(0.20) -1.709*
(0.29) 1.788***
(-1.04) 2.233***
(4.16) -0.150*** (-10.64)
(-1.35) -0.101*** (-6.68)
(-0.20) -0.078*** (-4.13)
(2.78) -0.091*** (-6.24) 0.479*** (15.77) 0.109*** (3.77) 1.789***
(2.18) -0.071** (-2.36) 0.366** (2.47) 0.139 (1.16) 1.160
(3.31) -0.183*** (-11.73)
(-1.75) -0.126*** (-7.45)
8.794***
(2.93) -0.078*** (-3.58) 0.626*** (4.26) -0.043 (-0.24) 1.396
(4.69) -0.116*** (-6.54)
5.599***
(3.96) -0.112*** (-9.71) 0.637*** (19.58) 0.010 (0.32) 0.741
6.031***
9.377***
(3.61) -0.132*** (-10.02) 0.615*** (18.67) 0.037 (1.10) 1.388**
(2.85) -0.094*** (-3.85) 0.637*** (4.90) -0.139 (-0.48) 2.102
Tenure t
A
Log(MV) t
CC E
Age t
ROA t
ED
Cash comp/1000 t-1
risk t-1 risk t-2 Constant
(4) GMM 0.186 (1.42) 0.029*** (4.30) -95.626* (-1.92) 0.000 (0.11) 0.000 (0.04) -0.005
(5) OLS -0.318*** (-4.69) 0.014* (1.74) 57.854*** (4.11) -0.009*** (-3.50) 0.005** (1.96) 0.074***
(6) FE -0.448*** (-6.03) -0.021** (-2.03) -54.161*** (-3.35) -0.001 (-0.30) 0.006 (1.44) -0.028
(7) DOLS -0.097* (-1.66) 0.008 (1.25) -0.725 (-0.05) -0.002 (-0.68) -0.000 (-0.16) 0.045***
(8) GMM 0.007 (0.04) 0.028*** (3.58) -138.130* (-1.76) -0.001 (-0.34) -0.000 (-0.09) 0.095***
(9) OLS 0.101* (1.70) 0.032*** (4.42) 45.981*** (3.71) -0.005** (-2.17) 0.002 (0.73) -0.178***
(10) FE -0.041 (-0.62) 0.003 (0.29) -19.307 (-1.34) -0.004 (-0.97) 0.008** (2.19) -0.256***
(11) DOLS 0.050 (0.98) 0.015** (2.47) 11.136 (0.97) -0.000 (-0.00) -0.000 (-0.07) -0.039***
(12) GMM 0.311* (1.74) 0.033*** (3.24) -96.319* (-1.66) 0.000 (0.04) 0.001 (0.20) -0.065
M
Market/Book t
Delta t-1
(2) FE -0.110* (-1.86) -0.003 (-0.31) -28.114** (-2.18) -0.005 (-1.38) 0.008** (2.36) -0.187***
Unsystematic Risk t
(3) DOLS 0.013 (0.29) 0.013** (2.51) 6.950 (0.68) -0.001 (-0.39) -0.000 (-0.20) -0.013
Vega t-1
(1) OLS 0.024 (0.44) 0.025*** (3.88) 49.981*** (4.46) -0.006*** (-3.00) 0.002 (1.09) -0.109***
Systematic Risk t
PT
VARIABLES
A
The columns represent the dependent variables – unsystematic, systematic, and total risks, and the four models, OLS, fixed-effects (FE), dynamic OLS (DOLS) and GMM. Compensation structure variables (Vega, Delta and cash compensation) are lagged one year. Control variables are CEO tenure, age, logarithm of market capitalization, market to book ratio, book value of leverage, and ROA. All the dynamic GMM models are based on 1058 observations from 15 years (1995 – 2009). 14 year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively. In GMM estimation, for first-differenced equations, the GMM instruments include the lagged vega, delta, and cash compensation from 3 years and further. For level equations, the GMM instruments again include the lagged differences of vega, delta and cash compensation from 2 years ago and further. AR(1) and AR(2) p-values are for tests of first and second-order serial correlation in the first-differenced residuals with the null of no serial correlation. Hansen’s J-statistic p-values are for over-identification test of the instruments in the differenced equations under the null that instruments are valid. The Diff-inHansen test p-values are for exogeneity of the instruments in the level equations with the null that all instruments are exogenous.
1.892***
5.661*** 40
(1.55) Yes 1,058 0.906
(0.89) Yes 1,058
0.00, 0.25 0.188 0.887
N U SC RI PT
(9.00) Yes 1,274 0.908
(3.22) Yes 1,274 0.828
(4.62) Yes 1,274 0.906
A
CC E
PT
ED
M
A
Year Dummies Observations R-squared AR(1)/AR(2) (p-value) Hansen’s J-stat (p-value) Diff-in-Hansen test (p-value)
(12.00) Yes 1,274 0.832
41
(3.21) Yes 1,058 0.890
(0.98) Yes 1,058
(11.68) Yes 1,274 0.788
(8.59) Yes 1,274 0.881
(2.55) Yes 1,058 0.875
(0.78) Yes 1,058
0.01, 0.91
0.00, 0.26
0.227
0.187
0.290
0.271
Table 5. The influence of commercial bank, large bank and bank with high leverage
SC RI PT
In this table, we report the dynamic panel GMM estimation results of the risk model with interaction terms between CEO compensation (Vega and Delta) and bank characteristics (dummies for commercial bank, large bank and bank with high leverage). Total risk, systematic risk and unsystematic risk are dependent variables in columns (1)-(3), respectively. Dummy variables SIC6020, LARGE, HIGHLEV are equal to one if the bank belongs to commercial bank, and bank-year observation has values above the median in bank size and book leverage ratio in the year, otherwise zero. vegat-1*SIC6020, vegat-1*LARGE, and vegat-1*HIGHLEV are interaction terms between lagged vega and the dummies for commercial bank, large bank and bank with high leverage ratio respectively. delta t-1*SIC6020, deltat-1*LARGE, and deltat-1*HIGHLEV are interaction terms between lagged delta and the dummies for commercial bank, large bank and bank with high leverage ratio respectively. In GMM estimation, for first-differenced equations, the GMM instruments include the lagged variables of vega, delta, and cash compensation from 3 years ago and further. For level equations, the GMM instruments include the lagged differences of vega, delta and cash compensation from 2 years ago and further. AR(1) and AR(2) p-values are for tests of first and second-order serial correlation in the residuals with the null of no serial correlation. Hansen’s J-statistic p-values are for overidentification test of the instruments in the differenced equations under the null that instruments are valid. The Diff-in-Hansen test pvalues are for exogeneity of the instruments in the level equations with the null that all instruments are exogenous. Year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively. Dynamic GMM with Interactions of Commercial Bank, Large Bank and High Leverage Total Riskt Systematic Riskt Unsystematic Riskt (1) (2) (3) vega t-1 -0.284 -4.495 -2.385 (-0.07) (-1.39) (-0.40) vega t-1*SIC6020 -0.427 1.682 -0.447 (-0.20) (0.95) (-0.19) vega t-1*LARGE 0.626 2.280 2.744 (0.25) (0.91) (0.63) vega t-1*HIGHLEV 0.517 0.938** 0.623 (1.25) (2.44) (1.24) delta t-1 0.721 1.250* 1.309 (1.01) (1.84) (1.40) delta t-1*SIC6020 -0.490* -0.423** -0.743** (-1.85) (-2.01) (-2.12) delta t-1*LARGE -0.230 -0.826 -0.557 (-0.47) (-1.46) (-0.85) delta t-1*HIGHLEV -0.327 -0.299* -0.526** (-1.54) (-1.74) (-2.07) (Cash comp/1000) t-1 -66.982 -63.472 -49.530 (-1.16) (-0.95) (-0.83) tenure t -0.005 -0.008 -0.006 (-0.81) (-1.17) (-0.69) Age t -0.000 0.001 0.002 (-0.01) (0.21) (0.35) Log(MV) t 0.022 0.138*** -0.006 (0.52) (3.29) (-0.07) Market/Book t -0.023 -0.003 -0.018 (-0.68) (-0.07) (-0.44) Leverage t 2.860** 2.498** 3.206** (2.45) (2.10) (2.33) ROA t -0.078*** -0.078** -0.091*** (-2.98) (-2.04) (-2.97) risk t-1 0.564*** 0.236* 0.580*** (4.06) (1.74) (3.82) risk t-2 0.106 0.096 0.067 (0.46) (0.72) (0.21) Constant 0.000 0.000 -0.731 (.) (.) (-0.20) Year Dummies Yes Yes Yes Observations 1,058 1,058 1,058 AR(1)/AR(2) (p-value) 0.00, 0.77 0.01, 0.80 0.00, 0.87 Hansen’s J-stat (p-value) 0.093 0.141 0.160 Diff-in-Hansen test (p-value) 0.564 0.175 0.696 (p-value) 42
A
CC
EP
TE
D
M
A
N
U
VARIABLES
S0148-6195(17)30080-2 https://doi.org/10.1016/j.jeconbus.2018.06.001 JEB 5812
To appear in:
Journal of Economics and Business
Received date: Revised date: Accepted date:
28-3-2017 1-6-2018 5-6-2018
Please cite this article as: Bharati R, Jia J, Do bank CEOs really increase risk in vega? Evidence from a dynamic panel GMM specification, Journal of Economics and Business (2018), https://doi.org/10.1016/j.jeconbus.2018.06.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Do bank CEOs really increase risk in vega? Evidence from a dynamic panel GMM specification1
SC RI PT
Rakesh Bharati, Jingyi Jia Rakesh Bharati Professor, Department of Economics and Finance, School of Business, Southern Illinois University – Edwardsville, Edwardsville, IL 62026, Email: [email protected], Tel: 618-650-2549
N
U
Jingyi Jia (Corresponding Author) Associate Professor Department of Economics and Finance, School of Business, Southern Illinois University – Edwardsville, Edwardsville, IL 62026, Email: [email protected], Tel:618-6502980
M
A
March 23, 2018
A
CC
No evidence for positive risk -CEO compensation vega relationship Strong evidence for positive risk - CEO compensation delta relationship Delta relation is driven by low-leverage banks which are less risk-averse. Delta relation is not in commercial banks and high-leverage bank.
EP
TE
D
Highlights
1
We sincerely appreciate the constructive comments and suggestions of the editor and two anonymous referees to help us improve the paper. 1
Abstract:
M
A
N
U
SC RI PT
Previous executive compensation studies find that firm risk increases in the risk-taking incentive (vega) of CEOs’ compensation packages. However, the standard methodology of two-stage least squares (2SLS) regression can suffer from invalid instruments. Using a dynamic panel generalized method of moments (GMM) specification to control for dynamic endogeneity, unobserved heterogeneity, and simultaneity (Wintoki, et al., 2012), we find no evidence of a positive relationship between risk and vega for banking firms. Furthermore, across institutions, CEOs’ payperformance sensitivity (delta) positively relates to the risk. Finally, high-leverage banks and commercial banks seem less prone to risk increases in delta relative to the entire sample of financial institutions. These results are important to investors, boards, regulators, and creditors, as they are all concerned with the risk of the financial institution.
CC
EP
1. Introduction
TE
D
Key words: CEO Compensation, Dynamic Panel GMM model, bank risk-taking JEL Classification: G21; G28; G32; G34; J33
Vega is the sensitivity of a CEO’s compensation to the risk of her firm’s stock and it is calculated
A
as the change in dollar CEO compensation for a one percent change in the annualized standard deviation of stock returns (Core and Guay, 2002). Delta, or pay-performance sensitivity, is the marginal impact of stock price changes on CEO compensation. Delta is calculated as the change in dollar CEO compensation for a one percent change in the stock price. The relationship between 2
risk-taking and CEO compensation (vega and delta) has profound implications for the entire economic system, including bank boards, capital providers, and regulators. Bank regulators such as Federal Reserve Bank (FRB) and the Federal Deposit Insurance Corporation (FDIC) need to
SC RI PT
monitor the CEO compensation for the safety and soundness of the banking system and economy. CEOs take less than optimal risk when given inadequate incentives for risk-bearing, while aggressive incentives result in excessive risk-taking. Both outcomes, if systemic, are economically undesirable, as they can result either in low economic growth, or in widespread financial distress and recession.2 If this relationship is not well understood, bank boards may be incorrectly using
U
vega and delta in the CEO compensation package decision to control the bank’s risk, and investors
N
and bond-rating agencies may also be overweighting vega in determining the institution’s risk.
A
Empirically, the limited evidence on compensation and bank risk is mixed. 3 With two-stage least
M
squares (2SLS) regression method, DeYoung, et al. (2013) document that banks where CEOs had high vega compensation took substantially large amounts of both systematic risk and unsystematic
D
risk during 1995-2006. However, Fahlenbrach and Stulz (2011) find bank performance during the
TE
financial crisis to be unrelated to CEOs’ vegas at the end of 2006. The evidence on risk-delta
EP
relationship is ambiguous too (Armstrong and Vashishtha, 2012; Coles et al., 2006; Fahlenbrach and Stulz, 2011).
CC
There is justification for the skepticism of standard models like 2SLS in the risk-incentive context.
A
Instrument validity is a concern in the highly endogenous environment of risk-governance and the
Accordingly, Basel Committee for Banking Supervision notes that “compensation systems contribute to bank performance and risk-taking, and should therefore be key components of a bank’s governance and risk management [Principles for Enhancing Corporate Governance, October 2010]. 3 For banks, Bai and Elyasiani (2013) also provide support for a positive risk-vega relation. For the corporate sample, multiple studies find a positive risk-vega relationship (Amadeus and Sadka, 2015; Anantharaman and Lee, 2014; Coles, et al., 2006; and Hagendorff and Vallascas, 2011). 2
3
economy, because the instrumental variables affecting risk through compensation are also very likely to affect risk directly. Second, simultaneous equation models cannot fully address the dynamic endogeneity between risk and compensation variables. This occurs when lagged values
SC RI PT
of risk affect the present compensation, and the present compensation affects the future risk. We study the risk-vega relationship using a dynamic panel generalized method of moments (GMM) specification motivated by Arellano and Bond (1991), and employed in a performance-
governance context by Wintoki et al. (2012). The key advantage of the model is that with predetermined variables (e.g., lagged variables) as instruments, strictly exogenous instruments are
U
not necessary. The model has the added advantage of addressing dynamic endogenity by including
N
lagged dependent variables in the regressors. In addition, the GMM approach provides formal
M
Difference-in-Hansen test of exogeneity).
A
tests of the validity and exogeneity of the instruments (Hansen’s test of over-identification and
D
We find no evidence supporting a significant risk-vega relationship. In particular, the positive
TE
risk-vega relationship is insignificant for total and systematic risk, and only marginally positive for unsystematic risk. Clearly, a correction of dynamic endogeneity yields different results from
EP
those with 2SLS regressions. The evidence of a positive risk-vega relationship found in corporate
CC
studies may not apply here, as banks are regulated and have high leverages.4 Another potential
A
reason for the insignificant risk-vega relationship is that most stock options held by bank CEOs
4
We would like to thank an anonymous referee for the suggestion to clarify the effect of leverage on risk-taking. First, risk-taking may decrease at high leverage levels due to the risk-aversion of the CEO (Carpenter, 2000; Lewellen, 2006). Second, high bank leverage may prompt bondholders to actively perform monitoring which may reduce risktaking in vega (John and Qian, 2003; and John et al., 2010). We are also aware that high leverage in the banking industry may lead equity holders to invest in very risky projects and provide CEOs with more stock and stock options to incentivize risk-taking (Ross et al., 2010; Harris and Raviv, 1991). 4
are well-in-the-money, making the CEOs more conservative in risk-taking (Fahlenbrach and Stulz (2011). Our second finding is that delta is positively associated with risk-taking across all risk categories,
SC RI PT
consistent with Fahlenbrach and Stulz (2011) in banking studies and Armstrong and Vashishtha (2012) in corporate studies. Therefore, a greater sensitivity of a CEO’s wealth to stock price motivates the CEO to take higher risk to improve the bank’s long-term performance, as this would improve the stock price and the CEO’s personal wealth. 5 This positive risk-delta relationship could be attributable to an expectation that the government will not let banks fail (too-big-to-fail
U
problem) and bank stock is similar to a call option, as the downside risk is eliminated or reduced.
N
Further, consistent with the theoretical prediction, we find that high leverage banks appear less
A
likely to increase risk in delta, compared to low leverage banks (e.g., Booth, et al., 2002; Lewellen,
M
2006; John, et al., 2010). Commercial banks also share this reduced propensity to risk taking in
D
delta. This can be viewed as a reconciliation of our results on delta with those in DeYoung et al.
TE
(2013) since that study is based on commercial bank sample. Our results are critically important to bank regulators, boards, and investors. Based on our
EP
findings, the FDIC must include compensation delta when pricing deposit insurance for a bank,
CC
and FRB should consider delta when auditing banks to detect excessive risk-taking. Bank boards should pay more attention to CEO compensation delta and they should not overly rely on
A
compensation vega to motivate the CEO to take the optimal level of risk. Bond rating agencies
Fahlenbrach and Stulz (2011) mentions (Page 12) that if CEO’s holdings of stock make him more conservative, higher vega would help in aligning the CEO’s incentives with those of shareholders by increasing risk. Since we find that delta mainly driven by stock holdings is still positively related to risk, it seems that CEOs are not at the stage of being conservative and the effect of vega is not very obvious. 5
5
and investors should also make use of the information in compensation delta to rate bank bonds and to trade bank stocks. Following the literature review in Section 2, hypothesis development and methodology are
SC RI PT
explained in Section 3. Data and the sample are described in Section 4. Primary results are presented in Section 5. In Section 6, we investigate the influence of bank characteristics. Section 7 concludes the paper. 2. Literature review
U
2.1. Theory and evidence on executive compensation
N
Compensation structure includes vega, delta, cash compensation, and other variables (e.g., pension
A
and other benefits). Core-Guay (1999, 2002) employ a one-year approximation method to
M
compute compensation package sensitivities. Vega represents the convexity of the compensation
D
package that incentivizes risk-taking. There are good reasons to doubt a universally positive risk-
TE
vega relationship. First, a positive risk-vega relationship is a comparative static of the BlackScholes option pricing model, which is derived under perfect, costless hedging, leading to a risk
EP
neutral valuation – assumptions that may not apply to a typical risk-averse CEO who may be trading and hedging constrained due to corporate policies, regulatory structures, and insider trading
CC
rules.6 Second, under managerial risk aversion, vega may be risk reducing or increasing depending
A
upon the moneyness of the options (e.g., Lambert, et al., 1991; Carpenter, 2000; Ross, 2004; Parrino et al., 2005; Lewellen, 2006). Specific to banks, regulatory supervision may curb
6
Early exercise of options, after vesting but long before their actual maturity, strongly support executive risk aversion (e.g., Huddart and Lang, 1996; Hemmer et al., 1996; Heath, et al., 1999; Hall and Murphy, 2002; Bettis et al., 2005). 6
independence and make risk-taking incentives less important or irrelevant (e.g., Booth, et al., 2002; John et al., 2000), as it could invite stronger regulatory scrutiny. The highly leveraged nature of banks prompts bondholders to actively perform monitoring, which may reduce risk-taking (e.g.,
SC RI PT
John and Qian, 2003; and John, et al., 2010). Also, banks that trade derivatives need high credit ratings, which may reduce risk-taking (Fahlenbrach and Stulz, 2011).
Empirically, using 2SLS modeling, Bai and Elyasiani (2013) find a positive relationship between vega and the insolvency risk proxied by the Z-Score. Similarly, DeYoung, et al. (2013) support a positive risk-vega relationship and find evidence of some implementation of risk policies in vega.
U
Hagendorff and Vallascas (2011) show that risky bank acquisitions increase in vega. Whereas the
N
above studies support the positive relationship, Fahlenbrach and Stulz (2011) focus on the crisis
A
years and show that CEO compensation vega across banks does not explain market or accounting
M
based performance measures – equity return, return on assets, and return on equity.
D
Delta could be risk enhancing, risk reducing, or neutral (Chava and Purnanandam, 2010;
TE
Fahlenbrach and Stulz, 2011; DeYoung et al., 2013; Berger, et al., 2016). On the one hand, highdelta compensation from large stock grants will align the interest of shareholders and the CEO,
EP
inducing higher risk-taking (Jensen and Meckling, 1976; John and John, 1993). In addition, the
CC
guarantee provided by FDIC may induce the CEO to prefer higher risk with higher delta compensation. On the other hand, a high delta may increase the wealth concentration of a CEO in
A
the firm’s stock, and induce greater risk aversion through non-diversifiable human capital. The evidence on risk-delta relation is ambiguous with Armstrong and Vashishtha (2012), Coles et al. (2006), and Fahlenbrach and Stulz (2011) producing supportive evidence for a positive
7
relationship, while Chava and Purnanadam (2010)
and DeYoung, et al.(2013) produce
contradictory results. Cash compensation, including cash salary and bonus, also has two conflicting effects on risk-
SC RI PT
taking (Guay, 1999; Coles et al., 2006). Berger et al. (1997) show that higher CEO cash compensation is associated with a lower leverage ratio and lower risk because the CEO wants to protect non-diversifiable human capital. However, Guay (1999) argues that cash compensation can be invested outside of the firm. Thus, the CEO is more diversified and may prefer higher risk
U
with higher cash compensation.
N
2.2. Methodological approaches employed in extant literature
A
Based on the insights offered by Wintoki et al. (2012) in the performance-governance relationship,
M
estimation of the risk-vega relationship entails three kinds of endogeneity issues: unobservable heterogeneity, simultaneity, and dynamic endogeneity. The following discusses the advantages of
TE
D
the dynamic GMM model in addressing these issues relative to other methodologies.
EP
2.2.1. Fixed-effects estimation to address unobservable heterogeneity Unobservable heterogeneity occurs when an omitted factor (e.g., managerial ability) affects both
CC
the dependent variable (risk-taking in our case) and the independent variable of interest (vega), and is commonly remedied through the use of fixed-effects estimation (e.g., Hermalin and
A
Weisbach, 1991; Himmelberg et al., 1999). 7 Given dynamic endogeneity, the fixed-effects estimation is not consistent and can reduce the power of the tests and produce biased estimation.
7
Himmelberg et al. (1999) show that regression of firm performance on firm policy or characteristics (or vice versa) may lead to spurious regression, as they are endogenously determined and that the exogenous variables (e.g., managerial abilities) crucial to the determination are not observable. Therefore, correction for endogeneity is critical. 8
This is because the assumption that current observations of the explanatory variable (vega and delta) are independent of past values of the dependent variable (risk variables) is not realistic (Wintoki et al., 2012). Compared to the fixed-effects regression model, the dynamic GMM panel
SC RI PT
specification produces unbiased estimates if there is a dynamic relationship between independent variables and lagged dependent variables. The dynamic GMM model accounts for unobservable heterogeneity by including firm fixed-effects in the model specification. 2.2.2. Simultaneous equations model to address simultaneity
U
Simultaneity occurs when the variables of interest (risk-taking and vega) are jointly determined,
N
and it is addressed through a simultaneous equation model (e.g., Rajgopal and Shevlin, 2002; Coles
A
et al., 2006; Armstrong and Vashistha, 2012; DeYoung, et al., 2013; Bai and Elyasiani, 2013).
M
Simultaneous equations models, though attractive, require strictly exogenous instruments that are very difficult to identify in a corporate finance setting where theory provides little guidance, as is
D
the case of executive compensation. For instance, Coles et al. (2006) use lagged and predicted
TE
values of vega and delta as exogenous instruments to address the endogeneity. By contrast, DeYoung et al. (2013) employ the following instruments – economic conditions, transient
EP
institutional ownership, past cumulative returns, salary, and tenure. While these variables may be
CC
related to vega and delta, it is difficult to argue that they have no direct influence on bank risk.
A
This possibility compromises their use as instruments.8
8
Some studies use the natural experiment approach to resolve the issue of endogeneity (e.g., Delaware Supreme Court’s 1995 Unitrin Inc. v. American General Corp. ruling that increased takeover protection in Low (2009)). Nevertheless, this approach comes with its own set of complications because natural experiments may not be truly exogenous. For example, regulatory or other changes may be designed specifically to obtain a certain outcome. Further, the changes could be anticipated, allowing for the environment and expectations to adjust. Indeed, Chava and Purnanandam (2010) and Hayes et al. (2012) reach different conclusions after conditioning on the 2004 FASB ruling on option expensing. 9
By contrast, the dynamic GMM model uses lagged dependent and independent variables as instruments. It essentially constrains the researcher from using an arbitrary set of instruments, which may just happen to be correlated with the variables of interest. Further, the approach
SC RI PT
provides formal tests of the validity and exogeneity of instruments, namely Hansen’s test of overidentification and the Diff-in-Hansen test. Similar tests are not formalized for simultaneous equation models. The dynamic GMM approach is also robust to heteroscedasticity and serial correlation, unlike the 2SLS approach.
U
2.2.3. Dynamic GMM model to address dynamic endogeneity
N
Dynamic endogeneity has heretofore been unaddressed in executive compensation studies. The
A
problem is caused by the dependence of the independent variables (vega or delta) on the lagged
M
values of the dependent variable (risk-taking) in the presence of unobservable effects (Wintoki et al., 2012). Using a dynamic panel GMM model originally motivated by Arellano and Bond (1991)
D
to account for dynamic and other forms of endogeneity, Wintoki et al. (2012) find no relationship
TE
between performance and board structure, unlike prior studies.
EP
Intuition suggests that dynamic endogeneity also exists in the relationship of risk-taking and CEO incentive compensation because compensation committees will structure the CEO compensation
CC
measures, such as vega or delta, based on the past risk level. Further, the performance goals and compensation structure are set through discussions between the board and the CEO, and her
A
bargaining position is affected by the past bank risk. Indeed, Pathan (2009) presents evidence that CEO power, measured through CEO duality and the founder or internal-hire status, is negatively related to bank risk-taking. DeYoung, et al. (2013) argue that bank boards take existing levels of market risk into consideration when they set CEO wealth incentives. 10
It is also empirically known that there is a degree of persistence in the bank (or corporate) performance measures, and Wintoki et al. (2012) uses lags of the dependent variables as controls to ensure a robust specification. Indeed, it is increasingly common to use a dynamic specification
SC RI PT
for bank risk. 9 Assuming compensation’s dependence on the past risk, the failure to include persistent lagged risk can lead to its effect being captured by the compensation structure variables, resulting in incorrect conclusions. 3. Hypothesis development and the econometric model
U
In the 1990s, compensation incentives became more relevant to the banking industry (Crawford,
N
et al., 1995; Hubbard and Palia, 1995) with the financial deregulation and rapid expansion of
A
banks.10 As DeYoung at al. (2013) show, while the average total compensation remained slightly
M
above that of non-banking firms, the dollar vega value of a CEO compensation contract increased rapidly relative to non-banks after 1994, peaked around 2003, and maintained this substantial
D
spread until 2006. This run-up partly supported the popular opinion that bank compensation
TE
practices were at least partly to blame for the excessive risk taking and the subsequent financial
EP
crisis.
We propose and test a relationship between the market measures of risk and the previous year
9
CC
compensation structure variables (vega, delta, and cash compensation) for banks. This lead-lag
A
Delis and Kouretas (2011) use a dynamic specification of risk in their study of bank risk and competition, where risk is measured as the nonperforming loan ratio. Ellul and Yerramilli (2013) use a dynamic panel GMM approach to model bank tail risk. Fiordelisi et al. (2011) also use lags of the nonperforming loan ratio, in addition to lagged expected default frequency. Koutsomanoli-Filippaki and Mamatzakis (2009) use the dynamic panel GMM to model the distance-to-default for a sample of European banks. 10 In the 1990s, the banking industry saw two major regulatory overhauls. First, the Riegle-Neal Interstate Banking and Branching Efficiency Act of 1994 was a step towards nation-wide banking, as restrictions on expansion across state line were eased. Next, by effectively repealing the ownership restrictions on bank holding companies, the Gramm-Leach-Bliley Financial Services Modernization Act of 1999 permitted entry into formerly excluded lines of business (e.g., brokerage and fund management, investment banking, and insurance). 11
relation is similar to Rajgopal and Shevlin (2002) and DeYoung et al. (2013). On the other hand, the lead-lag relation is different from Coles et al. (2006), who present results from a simultaneous specification of risk policies and compensation sensitivities. However, in their Table 9, they do
SC RI PT
present total risk regressed on lagged sensitivities as a robustness test. The advantage of this lead risk, lagged compensation structure specification is that it allows the implemented risk policies to influence the market perception of risk.
Our literature review discussion in Section 2 suggests that a positive risk-vega relationship may not exist for banks and the two other major components of the compensation structure – delta and
U
cash compensation – can be risk-decreasing or risk-enhancing. Also, cash compensation and delta,
N
with a few exceptions for delta, are usually employed in other studies as control variables, but we
A
treat them as variables of interest. This is consistent with the studies that indicate that boards may
M
be reluctant to reduce vega and may temper the CEO’s risk appetite with other components of the
TE
our hypothesis below.
D
compensation structure (e.g., DeYoung et al. (2013) on the use of delta). Therefore, we propose
EP
H1: Bank risk is unrelated to CEO compensation structure (vega, delta, and cash compensation). The Arellano and Bond (1991) methodology differences the original level equation, and then
CC
estimates the differenced equation with predetermined instruments in levels. However, as Wintoki et al. (2012) note, differencing may reduce variation in the data and decrease the power of the test,
A
and can make the measurement error problem more severe. Further, variables in levels may make weak instruments for the first-differenced equation. To address these potential shortcomings, the level equation is also included with the differenced equation in a system GMM model (Arellano
12
and Bover, 1995; Blundell and Bond, 1998). The first-differenced variables are the instruments for the equations in level. The estimated system GMM model is as follows:
SC RI PT
𝐸 (1) 𝑌 𝑌 𝑋 𝑍 ( 𝑡 ) = 𝛼 + 𝛽 ∗ ( 𝑡−𝑘 ) + 𝛾 ∗ ( 𝑡−1 ) + 𝛿 ∗ ( 𝑡 ) + 𝑡 𝑦𝑡 𝑦𝑡−𝑘 𝑥𝑡−1 𝑧𝑡 𝜀𝑡 (2) Y is the level dependent variable (the measure of risk in this study) and y is the first difference of Y (the risk measure less its one lag). X and x, in a similar fashion, indicate the level and the first difference of the independent variable (vega, delta and cash compensation in our case). The presence of minus one in the subscript of X and x indicates that current year’s risk measure is
U
being regressed on the explanatory variables at the end of the previous year. is the coefficient
N
that is hypothesized to be zero under H1 above. Z and z similarly indicate the control variables,
A
which include CEO age, CEO tenure, logarithm of market capitalization, book leverage ratio,
M
ROA and year dummies. 11 Finally, is an independently and identically distributed normal
D
variate with a zero mean, and its lower case counterpart () is its first difference. Note that the
EP
specification.
TE
model includes lagged dependent variables up to k further lags to account for a dynamic
The GMM instruments for the first-differenced equation include lagged levels of vega, delta and
CC
cash compensation older than two years (three years ago and further).12 The GMM instruments for the level equation are lagged differences of these three compensation variables older than one year
A
(two years ago and further). In our GMM estimation, following Wintoki (2012), we use the twostep estimation option to achieve greater asymptotic efficiency, compared to the one-step
11
Similar to Appendix B in Wintoki et al.(2012), these variables are the exogenous partition of the independent variables. In STATA, these variables are included in ivstyle( ), and called standard instruments. 12 Similar to Appendix B in Wintoki et al.(2012), these variables are the endogenous partition of the independent variables. In STATA, these variables are included in gmmsyle( ), and called GMM style instruments. 13
estimation option. We also use the robustness option to implement the finite-sample correction
SC RI PT
procedure (Windmeijer, 2005).13
4. Data, sampling and variable construction 4.1. Data
CEO related variables are from Standard and Poor’s ExecuComp database for banking firms (SIC
U
codes of 6020 for commercial banks, 6035 for federally chartered saving institutions, and 6036 for
N
state-chartered saving institutions). This data provides the information to construct vega and delta
A
for the sample period of 1993-2009. Stock volatility over the past five years and dividend yield
M
over the past three months are not available in the database after 2006 due to a change in SEC
D
reporting requirements. Therefore, we construct these two variables for the latter period using
TE
Standard and Poor’s methodologies.14 We construct bank risk measures (total, systematic, and unsystematic risk) with data from the Center for Research in Security Prices (CRSP). Other firm
EP
control variables are constructed from COMPUSTAT. The final sample used in the estimations has 1521 observations from 217 banks with complete data during 1993-2009. All GMM estimates
CC
are based on 1058 observations from 15 years (1995 – 2009). Observations from 1993 and 1994
A
are omitted due to the differencing.
13
For example, we use the following code for the estimation of the total risk model: xtabond2 risk_total l.risk_total l2.risk_total vega delta total_curr tenure age log(MV) Market/Book bookleverage ROA year_1993-year_2009, gmm(vega delta total_curr, lag (3 . ) collapse) iv(age tenure log(MV) Market/Book bookleverage ROA year_1994year_2009) twostep robust small. 14 We sincerely appreciate detailed instructions and great help from Lindsey Fenner, the senior product consultant from Standard and Poor’s. 14
4.2. Variable construction and descriptive statistics Our analysis employs three sets of variables, for which the descriptive statistics are presented in Table 1.
SC RI PT
4.2.1. CEO compensation sensitivities and other CEO related variables
Panel A of Table 1 contains the descriptive statistics for CEO related variables. Consistent with the literature, we assume the vega of stock holdings to be zero (e.g., Coles, et al., 2006). Cash compensation is the sum of salary and bonus. All compensation variables are in millions of dollars
U
and other CEO variables (tenure and age) are in years.
N
The mean (median) vega is $167,000 ($54,000) and the mean (median) delta is $700,000
A
($246,000). The right-skewed distribution supports the observation that large bank CEOs have
M
much larger vegas and deltas than all other CEOs in the sample. These figures are broadly
D
bracketed by those obtained in other studies, despite the sample differences. In the sample of Coles
TE
et al. (2006), vega and delta (with mean of $80,000 and $600,000, respectively) are smaller, and the same is true for the medians. However, we focus on banking firms while theirs is a corporate
EP
sample ending in 2002. On the other hand, our vega and delta means are lower than those in the
CC
study by DeYoung, et al. (2013): $215,849 and $893,688, respectively. They use a smaller sample of 114 commercial banking firms over the period of 1995-2006 (573 bank-years) while we employ
A
a much broader sample of 217 banks with 1,521 bank-years. Cash compensation of $1.4 million, on the other hand, is significantly lower than the $2.5 million reported in Coles, et al. (2006), and the $2.06 million in DeYoung, et al. (2013). These figures taken in sum suggest a proclivity of banks towards stock based compensation. Mean CEO tenure is 7.75 years in our sample, close to 7 years in Coles, et al. (2006), but lower than 9.9 years in DeYoung et al. (2013). The mean and 15
median of CEO age is 57, similar to the age of 54 reported in Coles, et al. (2006). If large cash compensation, tenure, and age are indicators of entrenchment, we cannot claim that bank CEOs are more entrenched than those in nonfinancial firms.
SC RI PT
4.2.2. Risk measures We constructed the total, systematic, and unsystematic risk variables similar to Low (2009). All sample fiscal years end in December. Total risk is the natural logarithm of the annualized variance of daily returns over a year. Systematic risk is the natural logarithm of the annualized variance of
U
the predicted portion of the market model, which regresses individual stock returns on CRSP
N
value-weighted market portfolio returns, and its five lags and leads to adjust for non-synchronous
A
trading (Low, 2009). Unsystematic risk is the natural logarithm of the annualized variance of the
M
residuals of the market model. As shown in Panel B of Table 1, the mean and median values of the risk variables are close. In comparison to Low (2009), the statistics of our total risk and
D
unsystematic risk variables are broadly similar, despite a large difference in the sample.
TE
Interestingly, our log-transformed total risk mean of 6.84 is consistent with the mean of 0.017 in DeYoung et al. (2013), after applying the appropriate log-transformation to their decimal daily
EP
standard deviation without log transformation. The same consistency also holds for the median of
CC
total risk, and the mean and the median of unsystematic risk.
A
4.2.3. Firm-specific control variables Following Coles et al. (2006), we include firm size, market-to-book ratio of equity, book leverage ratio, and return on asset (ROA) as firm-specific control variables. Market capitalization, calculated as fiscal year-end stock price multiplied by the number of common shares outstanding, is the proxy for firm size. The market-to-book ratio is the ratio of market value of equity to book 16
value of equity. A higher market-to-book ratio indicates higher growth opportunities, and is expected to be positively related to firm risk. The book leverage ratio is the ratio of total debt to assets, and it relates positively to risk. ROA is presented as a percent and is defined as net income
SC RI PT
before extraordinary items and discontinued operations divided by total assets. In Panel C of Table 1, the statistics for the market-to-book ratio are similar to those in Coles et al. (2006) and DeYoung et al. (2013). Our mean (median) book leverage ratio of 0.91 (0.92) is much higher than the 0.23 (0.21) reported in Coles et al. (2006), as they excluded financial firms and utilities. However, our leverage ratio is nearly identical to the complement of the equity ratio in DeYoung, et al. (2013):
U
0.084 (0.083) for the mean (median). Typically, banks have much higher leverage ratios than
N
nonfinancial firms. Though large, our mean (median) book leverage actually indicates that our
A
banks are generally well-capitalized based on the FDIC requirements.15
M
Panel D of Table 1 presents the correlation coefficients between the various variables. The risk
D
measures are strongly correlated with one another. In addition, total and unsystematic risks are
TE
negatively correlated to the compensation structure variables (vega, delta and cash compensation), while systematic risk is positively related to them, with some cases of significance. This suggests
EP
that risk during the year is related to the compensation structure variables at the end of the year. Generally, the correlations between firm control variables, risk measures, and compensation
A
CC
sensitivities are strong and significant. 16
According to the FDIC Improvement Act in 1991, if a bank’s capital-asset ratio is above 5 percent and total riskbased ratio and Tier 1 risk-based ratio is above 10 percent and 6 percent respectively, it is well capitalized and is placed in the highest capital adequacy zone. 16 We would like to thank an anonymous referee and the editor for the suggestion to acknowledge the potential influence of outliers due to the extreme values of delta and leverage. Since winsorizing procedure will reduce our random sample, we conduct the tests with the full sample. If we winsorize the full sample only by 1 st and 99th of leverage ratio, all the results hold. If we further winsorize the full sample according to vega and delta, the results of delta become much weaker. 15
17
5. Empirical Results 5.1. Dependence of the compensation structure on past performance The presence of dynamic endogeneity is the key motivation for this study because we believe that
SC RI PT
the present compensation structure depends on the past risk-taking. Dynamic endogeneity is problematic as it causes the contemporaneous explanatory variables (vega, delta, cash compensation and even control variables) to be correlated with the lagged values of the error terms even though they are independent of the present error term. As indicated in Wintoki et al. (2012), with dynamic endogeneity, a fixed-effects regression of y on x could result in a statistically
N
U
significant coefficient for x even without a causal effect of x on y.
A
Accordingly, we test if our sample indicates the presence of dynamic endogeneity. We investigate
M
if the present compensation structure are related to past risk levels through OLS regressions of compensation variables (vega, delta and cash compensation) on lagged risk variables (total,
D
systematic and unsystematic risk). Table 2 presents the results where regressions of the levels of
TE
compensation variables are presented in Panel A, and the regressions of the changes in compensation variables are presented in Panel B. Panel A clearly shows a strong dependence of
EP
year-end compensation variables on lagged risk. In all cases, compensation structure variables –
CC
vega, delta and cash compensation – are significantly related to the risk variables in the recently completed year (at the 95 percent confidence level or better). In addition, the sign of the
A
relationship is uniformly positive with the only exception being the negative relationship between vega and systematic risk (column 2). Thus, delta, cash compensation, and vega are mostly positively associated with past levels of risk (total, systematic and unsystematic). Our results are consistent with the results of DeYoung et al. (2013) where the natural log of delta is positively 18
associated with the past level of total, systematic, and unsystematic risks in a 2SLS estimation framework. Thus, the evidence supports that the compensation structure is related to past risk levels.
SC RI PT
Panel B of Table 2 presents results of regressions similar to Panel A. However, the dependent compensation structure variables are differenced and regressed on past levels of risk and control variables. Once again, changes in delta, vega, and cash compensation are positively related to the past year’s risk levels, with traditional significances for delta and cash compensation. Therefore, boards may be responding to prior-year increases in risk levels by offering the CEO a higher delta
U
and cash compensation compared to the previous year (Berger et al., 1997; DeYoung et al., 2013;
N
Chava and Purnanandam, 2010). The relationship of the change in vega and the lagged risk is
A
positive, but significant only for the case of total risk at the 90 percent confidence level. These
M
generally uniform and strong findings in levels and first differences lend strong support to our
D
claim of dynamic endogeneity in the compensation structure.17
TE
5.2. Choosing the dynamic specification and appropriate lags for predetermined variables
EP
There are at least two reasons to conduct the tests to determine how many lags are needed in a dynamic specification (Wintoki et al., 2012).
First, the appropriate number of lags of risks to
CC
include in the model of dynamic panel GMM will insure dynamic completeness. Including too many lags will lead to overfitting, while having too few will fail to capture all past influences.
A
Therefore, including lagged risk as an explanatory variable for the current risk should help address the problem of misspecification.
17
We also ran regressions similar to Table 6 of Wintoki et al. (2012) to study the effect of risk on the future compensation. Our results, though not reported here, support the inference from Table 2. 19
While Delis and Kouretas (2011) employ one lag of risk, the literature investigating profitability of companies typically has included two lags of profitability (Gschwandtner, 2005; Wintoki et al., 2012). To decide, we run the risk measures on their four lags and control variables to determine
SC RI PT
the appropriate lag length. In the regressions with four lags of risk (columns 1, 3, and 5 of Table 3), only the first lag of risk is strongly significant for the total and unsystematic risks, and only the first two lags are strongly significant for the systematic risk, at the 99 percent confidence level. Furthermore, the model explains all three measures of risk well, with R2 measures in the vicinity of 90 percent. Therefore, using no more than two lags of risk should parsimoniously lead to
U
dynamic completeness. In the absence of the first two lags of risk, the next two lags become
N
strongly significant at mostly a 99 percent confidence level (columns 2, 4, and 6 of Table 3). The
A
R2 values remain at a comparable 85 percent or above. Therefore, the model advocates using the
M
third and fourth lags as predetermined instruments because they clearly are exogenous to the present period under the dynamic specification (i.e. with the first two lags of risk included in the
TE
D
dynamic panel for completeness).
5.3. The relationship between risk-taking and compensation structure
EP
Having established dynamic endogeneity and a dynamic specification, we now proceed to estimate
CC
the risk-compensation structure relationship as per the methodology outlined earlier. Consistent with Wintoki et al. (2012), we estimate four separate models – OLS, fixed-effects estimation,
A
dynamic OLS (DOLS) including lagged risk as controls, and dynamic GMM – to illustrate the advantages of the dynamic GMM approach by showing the differences across methodologies. OLS and dynamic OLS cannot address the bias due to unobservable heterogeneity. OLS and fixed-
20
effects estimation cannot address the dynamic relationship that the current independent variables (vega and delta) are related to the lagged dependent variable (risk). Table 4 presents the results across the four models for the three forms of risk. With the OLS model
SC RI PT
in columns 1, 5, and 9, the two risk components of unsystematic and systematic risks show mutually inconsistent relationships to vega.
Systematic risk is negatively related to vega
(significant at 99 percent), while unsystematic risk is positively related to vega with a marginal significance.
As a result, total risk has a small and insignificant coefficient on vega. The
relationship with delta demonstrates remarkable consistency, though. The three types of risk
U
positively relate to delta, with significances at 99 percent for total and unsystematic risks. Cash
N
compensation is positively related to the three forms of risk at 90 percent or better. However,
A
unobservable firm-level heterogeneity casts doubt over these results, and we next present fixed-
M
effects regressions to remove firm level heterogeneity.18
D
Estimation results of fixed-effects models are presented in columns 2, 6, and 10 of Table 4.
TE
Wintoki et al. (2012) presents an important critique of fixed-effects regressions in a dynamic context. They hypothesize and empirically show that the fixed-effects regression of y on x will be
EP
negatively (positively) biased if x is positively (negatively) related to lagged y values (See Eq. 5,
CC
and Tables 6 and 7 of their paper). 19 Our context is also dynamic, and we find a very similar result. As shown in Panel A of Table 2, we found that vega, delta, and cash compensation
A
positively relate to the three forms of lagged risk, barring the only exception of vega and systematic
18
Financial institutions have their own unique culture and CEOs differ in managerial ability and aggressiveness. As an example, aggressive CEOs or institutions may engage in substantial unsystematic risk-taking despite low vegas. 19 Wintoki et al. (2012) analytically show that fixed-effects estimation coefficients of performance-governance relation will be negatively biased if governance variables are positively related to lagged value of performance variables (i.e., a dynamic model), and provide empirical support for this hypotheses through their Table 6. 21
risk (column 2). In columns 2, 6 and 10 of Table 4, all nine fixed-effects estimation coefficients (three types of risk and three compensation variables) except one (coefficient of delta in column 10) are negative. Therefore, we conclude that the obtained fixed-effects coefficients are negatively
SC RI PT
biased as the methodology ignores the dynamic relationship between risk and compensation variables. However, removal of firm-level heterogeneity through firm dummies clearly yields a better fit as the R2 is higher by at least seven percent compared to OLS regressions. The fixedeffects estimation underscores the need for a dynamic panel GMM that can admit firm fixedeffects, while addressing dynamic endogeneity.
U
Next, we include two lags of risk and perform dynamic OLS estimation (columns 3, 7 and 11 of
N
Table 4). Note that there is no correction for endogeneity yet. One lag of risk is a strong predictor
A
of the current values of the three types of risk, as the coefficient at the first lag is positive and
M
significant at the 99 percent confidence level. The R2 is higher by at least seven percent, once again
D
compared to the OLS regressions. Vega is now unrelated to unsystematic and total risks, but
TE
negatively related to systematic risk with a marginal significance at 90 percent. For delta, the result is more interesting for unsystematic and total risks: delta appears to encourage unsystematic
EP
risk taking, which also increases total risk. Cash compensation does not appear to affect risk taking in any of the three forms of risk. Even without a correction for endogeneity, dynamic OLS suggest
CC
that vega and cash compensation do not appear to be related to risk-taking, but delta does.
A
With the dynamic panel GMM estimation to correct for endogeneity, we see a strong consistency between risk and vega in columns 4, 8 and 12 of Table 4. The coefficient on vega is always positive but marginally significant at 90 per cent only in the case of unsystematic risk (column 12). Thus, the null hypothesis of no risk-vega relationship cannot be rejected. This result is consistent 22
with that of Fahlenbrach and Stulz (2011) indicating that risk aversion of bank CEO, regulatory supervision and monitoring by bondholders mitigate the risk-taking incentives from vega. As explained in Fahlenbrach and Stulz (2011), given most of the CEO’s option holdings are in-the-
SC RI PT
money, the risk incentive from option compensation (vega) is similar to that from stock compensation and the CEO becomes more conservative (Ross, 2004; Carpenter, 2000).
For the risk-delta relationship, there is consistent and strong evidence across the board with the dynamic GMM model. In columns 4, 8 and 12 of Table 4, delta increases all three risks at 99 percent confidence levels, leading us to reject our null hypothesis of no relationship. The
U
significant positive relationship between bank risk and delta suggests that large stock grants in the
N
banking industry align the interest of a CEO with that of shareholders to improve the long-term
A
performance of the bank. This increased risk taking in delta found in our study is contrary to
M
DeYoung et al. (2013) who document a risk-inhibiting effect of delta using 2SLS with a
D
commercial bank sample, but it is consistent with several other studies with both financial and
TE
nonfinancial samples (Fahlenbrach and Stulz, 2011; Armstrong and Vashishtha, 2012; Coles et al., 2006). For example, Fahlenbrach and Stulz (2011) show that firms with high-delta CEOs
EP
performed worse during the crisis years, implying a positive risk-delta relationship. Our results are also consistent with Armstrong and Vashistha (2012) and Coles et al. (2006) in terms of the sign
CC
and significance of the coefficient of delta, though they use delta as a control variable and their
A
sample is nonfinancial firms. Our results support the argument of Saunders et al. (1990) that, as long as managerial ownership is not too high to make managers very sensitive to the undiversifiable risk of human capital, CEOs in shareholder-controlled banks, which align the
23
incentives of the managers with those of the shareholders through stocks and stock options, take higher risk. 20 In Columns 4, 8 and 12 of Table 4, cash compensation carries negative signs for all three measures
SC RI PT
of risk but the significances are consistently marginal (at the 90 percent level), providing weak evidence against the null hypothesis of no relationship. These general negative coefficients may support the argument by Berger et al.(1997) that higher cash compensation makes bank CEOs more conservative. Empirically our results on cash compensation are consistent in sign with those reported in Armstrong and Vashishtha (2012) and Coles et al. (2006), suggesting that higher cash
U
compensation leads CEOs to avoid risk to protect their human capital. We separated cash
A
M
coefficient on bonus remained insignificant.
N
compensation into salary and bonus, as bonus can be a risk-increasing device. However, the
The economic significances of the coefficients in columns 4, 8 and 12 are modest as well. A one
D
standard deviation increase of vega (0.314 million dollars) is associated with 0.10 standard
TE
deviation increase of unsystematic risk.21 One standard deviation of delta (2.203 million dollars) increases total, systematic, and unsystematic risks by 0.07, 0.05, and 0.08 standard deviation of
A
CC
EP
these three risks respectively.22 For cash compensation, a one standard deviation decrease of cash
20
Though ex-post in nature and not presented here, we also checked our sample to find bank holding companies (BHC) where at least a subsidiary failed during the financial crisis. Our sample contains only seven BHCs with failed subsidiaries that account for 46 observations. Removing these observations leaves the estimates largely unchanged. 21 Unsystematic risk increases by 0.097654 (=0.311*0.314). The standard deviation of unsystematic risk is 0.956 and this increase is equal to 0.10 standard deviation (0.097654/0.956=0.102). 22 Total risk increases by 0.07 standard deviation (2.203*0.029 = 0.063887; 0.063887/0.971=0.066), systematic risk increases by 0.050 standard deviation (2.203*0.028=0.061684; 0.061684/1.245=0.049545), and unsystematic risk increases by 0.076 standard deviation (2.203*0.033=0.072699; 0.072699/0.956=0.076). 24
compensation (1.448 million dollars) is related to 0.14, 0.16, and 0.15 standard deviation increases of these three risks respectively.23 In the specification tests presented at the bottom of Table 4, the p-values of the AR(2) tests are at
SC RI PT
least 0.25 across all three forms of risk. Therefore, the null hypothesis of no second-order serial correlation cannot be rejected. This satisfies the Arellano and Bond (1991) requirement of no serial correlation beyond one lag, and justifies the use of the predetermined variables as instruments. Hansen’s J-statistic, that tests overidentifying restrictions, has relatively large pvalues of higher than 18 percent for all three forms of risks. Therefore, the null hypothesis that
N
U
our instruments are valid cannot be rejected.
A
As explained in model specification in Section 3, we include the level equation in the system GMM
M
estimation following Arellano and Bover (1995) and Blundell and Bond (1998). The introduction of the level equation adds new instruments in the model, and we need to ensure that this subset of
D
instruments is also exogenous. Here, Difference-in-Hansen test of exogeneity provides further
TE
support, as the p-values are uniformly in excess of 0.27. Therefore, the exogeneity of additional instruments, our null hypothesis, cannot be rejected. This assures that the introduction of the level
EP
equation in the system GMM does not adversely affect the estimation.
CC
Before advancing to the next section, we address the concern if the results of Table 4 are driven by the outliers of vega, and delta. Large banks provide their CEOs with compensations that are
A
significantly higher than the typical bank CEO compensation. This pattern for delta and vega is evident in Table 1 as the gap between quartiles is enormous for the top quartile (75 percentile to
23
Total, systematic and unsystematic risks decrease by 0.14 standard deviation (-95.626*1.448/1000= -0.138466; 0.138466/0.971= -0.1426), 0.16 standard deviation (-138.130*1.448/1000= -0.2; -0.2/1.245=-0.1606), and 0.15 standard deviation (-96.319*1.448/1000 = -0.13947; -0.13947/0.956= -0.14589), respectively. 25
maximum), relative to the other quartiles. We address this concern in two different ways. First, we delete all observations for banks with assets greater than $100 billion (156 observations). The resulting GMM estimation, not presented here but available from the authors, provides
SC RI PT
substantially the same results as in Table 4. Vega is unrelated to all three forms of risk, while delta is positively related to all three forms of risk with significances of at least 95 percent confidence level. Next, we compute vega and delta as percentages of total compensation and re-estimate Table 4. Our results largely stand as total risk and unsystematic risk are still significantly and positively dependent on delta (though the delta coefficient for systematic risk is now negative but
N
while it is significantly negative for systematic risk.
U
insignificant). Likewise, the coefficient on vega is insignificant for total and unsystematic risks,
M
A
6. The influence of the commercial bank sample, bank size and leverage Our primary result is that bank risk is positively related to delta but unrelated to vega. However,
D
the result could be affected by bank characteristics such as different types of depository
TE
institutions, bank size, and bank leverage. First, with a sample of commercial banks, DeYoung et al. (2013) study the bank risk-vega relationship and document that vega encourages risk-taking,
EP
while delta curbs it. We instead find a contrary result with our comprehensive sample including
CC
commercial banks, federally chartered savings institutions (SIC code = 6035) and state-chartered savings institutions (SIC code = 6036). Second, large banks are different from small banks in terms
A
of business model: large banks engage more in risky nontraditional banking businesses (investment banking, security brokerage, and securitization), while small banks generally rely on the traditional “originate-to-hold” lending model and control their credit risk by intensive monitoring and maintaining long-term lending relationships with their customers (DeYoung and 26
Torna, 2013). It is possible that CEOs in large and small banks have different compensation incentive mechanisms, which might drive our primary result. Third, excessive bank leverage has always been an issue of concern, and the Basel III accord and the recent bank regulation seek to
SC RI PT
encourage banks to carry more equity to control risk-taking. Therefore, we now incorporate three key bank characteristics into our tests.
We explore if different types of depository institutions, bank size and leverage affect the positive risk-vega relationship through the use of dummy variables. We assign the dummy variable SIC6020 a value of one for commercial banks. Otherwise, the variable is assigned a value of zero
U
(savings institutions). Second, we define a bank size dummy by its capitalization. We annually
N
rank banks in order of size at the beginning of the calendar year, and assign the top half to large
A
banks. The indicator variable LARGE equals one for large banks (zero otherwise). A third dummy
M
variable (HIGHLEV) is defined as one if the bank has a higher leverage ratio than the sample
D
median value in each year (zero otherwise).
TE
We include the interactions of the three dummy variables with vega and delta into the dynamic GMM model, and the estimation results are reported in Table 5.
First, vega is no longer
EP
significantly related to risk in its three forms (unsystematic, systematic, and total), even at the 90
CC
percent confidence level. In Table 4, it was marginally positively related to the unsystematic risk. The coefficient of the interaction term between leverage and vega (Vegat-1*HIGHLEV) is positive
A
for the three forms of risk, but only significant for systematic risk at the 95 percent confidence level. This indicates that, for high leverage institutions, CEO compensation vega appears to positively increase systematic risk. Regulators should pay close attention to option grants in banks with inadequate capital since the associated high pay-risk sensitivity (vega) may lead to excessive 27
systematic risk-taking. The results of the vega interaction of the other two characteristics (SIC6020 and LARGE) are uniformly insignificant. Further, the positive risk-delta relation, previously obtained in Table 4, is significantly weakened
SC RI PT
after the inclusion of the three indicator variables, though the coefficient of delta by itself is still positive and marginally significant at the 90 percent confidence level in the model of systematic risk in Table 5. This is consistent with our primary result in Table 4, which indicates that a greater sensitivity of the CEO’s wealth to stock price (larger delta) motivates the CEO to take higher systematic risk to improve bank performance and associated CEO wealth for the entire sample.
U
Interestingly, interactions of delta with SIC6020 and HIGHLEV carry negative signs across all
N
three risk models indicating that commercial bank and high-leverage bank CEOs demonstrate a
A
reduced incentive for risk-taking in delta. The coefficients of the interaction terms between
M
SIC6020 and delta for systematic and unsystematic risks are significant at the 95 percent
D
confidence level, though total risk only has marginal significance at the 90 percent confidence
TE
level, indicating that commercial banks reduce risk-taking in delta compared to savings institutions. This result is consistent with that of DeYoung et al. (2013) who found that delta is
EP
negatively related to risk-taking in the commercial bank sample.
CC
The coefficients of the interaction terms between the leverage indicator variable and delta (deltat1*HIGHLEV)
are all negative. Here the interaction of delta with HIGHLEV is only marginally
A
significant at the 90 percent confidence level for systematic risk, and at the 95 percent confidence level for unsystematic risk. Therefore, compensation delta discourages risk-taking for highleverage firms. So, why do low-leverage bank CEOs take risk in compensation delta, but not the high-leverage bank CEOs? According to Fahlenbrach and Stulz (2011), a higher delta (sensitivity 28
of a CEO’s wealth to stock price) motivates the CEO to improve her bank’s long-term performance, which is reflected on stock price. Empirical evidence generally supports that lower leverage level (higher capital ratio) is associated with better bank performance (see buy-and-hold
SC RI PT
returns in Fahlenbrach and Stulz (2011) and survival and market share in Berger and Bouwman (2013)). Therefore, it is very likely that the low-leverage bank CEO takes risk in delta to enhance long-term bank performance, whereas the high-leverage bank CEO becomes more conservative and reduces risk-taking in delta to mitigate the detrimental effect of high leverage on bank performance. Furthermore, as noted earlier, academic theory offers several compelling reasons.
U
First, bondholders may aggressively monitor high-leverage banks which may reduce risk-taking
N
in compensation delta (e.g., John and Qian, 2003; John et al., 2010). Second, at high leverage
A
levels, rating agencies may be more sensitive to the CEO’s compensation delta and the CEO starts
M
to curb risk-taking. In addition, aggressive supervision of high leverage banks might make risktaking incentives less important or irrelevant (e.g., Booth et al., 2002). 24 In terms of model
EP
7. Conclusion
TE
specified model.
D
specification, the robustness statistics for the dynamic panel GMM estimation indicate a well-
CC
Convexity of the compensation package motivates CEOs to accept risky positive-NPV projects that they might otherwise forego. Using different samples of firms excluding financial institutions
A
and utilities, prominent studies find strong empirical support for the foregoing assertion. Nevertheless, convincing arguments exist that financial institutions, due to regulatory supervision
24
However, we need to be also aware that high leverage in the banking industry may motivate a CEO to take excessive risk in delta, because payoffs to the equity holder of a levered firm resemble those of a call option. This is due to the risk-shifting incentive to the equity holder to take advantage of the debtholder (Ross et al., 2010; Harris and Raviv, 1991). 29
and high leverage, might have a weaker or non-existent risk-vega relationship. Also, Carpenter (2000), Ross (2004), and Lewellen (2006), among others, model a risk-averse CEO and challenge the above assertion by showing that the risk-vega relationship may not always be positive. Finally,
SC RI PT
empirical evidence of early exercise, motivated by moneyness and vesting, strongly supports the view of a risk-averse CEO (Huddart and Lang, 1996; Hemmer et al., 1996; Heath, et al., 1999; Hall and Murphy, 2002; Bettis et al., 2005).
Our dynamic panel GMM estimator finds significant evidence that, for financial institutions in aggregate, risk increases in compensation delta, but not in vega. This result is similar to the crisis-
U
period analysis of Fahlenbrach and Stulz (2011). Our results differ from DeYoung et al. (2013)
N
who find vega to be risk increasing and delta to be risk moderating. However, institutional
M
A
CC
EP
TE
D
delta, unlike the aggregate result.
A
characteristics matter. Commercial banks and high leverage institutions tend to reduce risk in
30
Reference
SC RI PT
Amadeus, M., Sadka, R.(2015). Executive compensation convexity and firm crash risk. Available at SSRN: https://ssrn.com/abstract=2625852 or http://dx.doi.org/10.2139/ssrn.2625852 Anantharaman, D., Lee, Y.G.(2014). Managerial risk taking incentives and corporate pension policy. Journal of Financial Economics, 111(2), 328-351. Arellano, M., Bover, O.(1995). Another look at the instrumental variable estimation of errorcomponent models. Journal of Econometrics, 68, 29–51.
U
Arellano, M., Bond, S.(1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations, Review of Economic Studies, 58 (2), 277-297.
N
Armstrong, C.S., Vashishtha, R.(2012). Executive stock options, differential risk-taking incentives, and firm value, Journal of Financial Economics, 104(1), 70-88.
M
A
Bai, G., Elyasiani, E. (2013). Bank stability and managerial compensation. Journal of Banking & Finance 37, 799-813.
D
Berger, A, Imbierowicz, B., Rauch, C. (2016). The roles of corporate governance in bank failures during the recent financial crisis. Journal of Money, Credit and Banking, 48, 729–770.
TE
Berger, A. N., Bouwman, C. H.S.(2013). How does capital affect bank performance during financial crises? Journal of Financial Economics 109, 146-176.
EP
Berger, P., Ofek, E., Yermack, D.(1997). Managerial entrenchment and capital structure decisions. Journal of Finance 52, 1411-1438.
CC
Bettis J. C., Bizjak, J. M., Lemmon, M. L.(2005). Exercise behavior, valuation, and the incentive effects of employee stock options, Journal of Financial Economics, 76(2), 445-470.
A
Black, F., Scholes, M.(1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654. Blundell, R., Bond, S.(1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87, 115–143. Booth, J. R., Cornett, M. M., Tehranian, H.(2002). Boards of directors, ownership, and regulation. Journal of Banking and Finance, 26, 1973-1996.
31
Carpenter, J. (2000). Does option compensation increase managerial risk appetite? The Journal of Finance, 55(5), 2311-2331. Chava, S., Purnanandam, A.(2010). CEOs versus CFOs: Incentives and corporate policies. Journal of Financial Economics, 97(2), 263-278.
SC RI PT
Coles, J.L., Daniel, N.D., Naveen, L.(2006). Managerial incentives and risk-taking. Journal of Financial Economics, 79, 431-468. Core, J., Guay, W.(1999). The use of equity grants to manage optimal equity incentive levels. Journal of Accounting and Economics, 28, 151-84.
Core J., Guay, W.R.(2002). Estimating the value of executive stock option portfolios and their sensitivities to price and volatility. Journal of Accounting Research, 40, 613–630.
U
Crawford, A. J., Ezzell, J. R., & Miles, J. A.(1995). Bank CEO pay-performance relations and the effects of deregulation. Journal of Business, 68(2), 231-256.
A
N
Delis, M.D., Kouretas, G.P.(2011). Interest rates and bank risk-taking. Journal of Banking &Finance, 35(4), 840-855.
M
DeYoung, R., Peng, E., Yan, M.(2013). Executive compensation and business policy choices at U.S. commercial banks. Journal of Financial and Quantitative Analysis, 48(1), 165-196.
D
DeYoung, R., Torna, G.(2013). Nontraditional banking activities and bank failures during the financial crisis. Journal of Financial Intermediation 22, 397-421.
TE
Ellul, A. and Yerramilli, V. (2013). Stronger Risk Controls, Lower Risk: Evidence from U.S. Bank Holding Companies. The Journal of Finance, 68, 1757-1803.
EP
Fahlenbrach, R., Stulz, R.(2011). Bank CEO incentives and the credit crisis. Journal of Financial Economics, 99, 11-26.
CC
Fiordelisi, F., Marques-Ibanez, D., Molyneux, P.(2011). Efficiency and risk in European banking. Journal of Banking and Finance, 35(5), 1315-1326.
A
Gschwandtner, A.(2005). Profit persistence in the ‘very’ long run: evidence from survivors and exiters. Applied Economics 37, 793–806. Guay, W.R. (1999). The sensitivity of CEO wealth to equity risk: An analysis of the magnitude and determinants. Journal of Financial Economics, 53, 43–71. Hagendorff, J., Vallascas, F. (2011). CEO pay incentives and risk-taking: Evidence from bank acquisitions. Journal of Corporate Finance, 17(4), 1078-1095. 32
Hall, B.J., Murphy, K.J. (2002). Stock options for undiversified executives. Journal of Accounting and Economics, 33, 3–42. Harris, M., Raviv, A. (1991). The theory of capital structure. Journal of Finance 46:297–355. Hayes, R. M., Lemmon, M., Qiu M. (2012). Stock options and managerial incentives for risk taking: Evidence from FAS 123R. Journal of Financial Economics, 105, 174-190.
SC RI PT
Heath, C., Huddart, S., Lang, M.(1999). Psychological factors and stock option exercise, Quarterly Journal of Economics, 114, 601-628.
Hemmer, T., Matsunaga, S., Shevlin, T.(1996). The influence of risk diversification on the early exercise of employee stock options by executive officers. Journal of Accounting and Economics, 21(1), 45-68.
U
Hermalin, B.E., Weisbach M.S.(1991). The effects of board composition and direct incentives on firm performance. Financial Management, 20(4), 101-112.
A
N
Himmelberg, C., Hubbard, R.G., Palia, D.(1999). Understanding the determinants of managerial ownership and the link between ownership and performance, Journal of Financial Economics, 53(3), 353-384.
M
Hubbard, R.G., Palia, D.(1995). Executive pay and performance evidence form the U.S. banking industry. Journal of Financial Economics, 39, 105-130.
D
Huddart S., Lang M. (1996). Employee stock option exercises an empirical analysis. Journal of Accounting and Economics, 21(1), 5-43.
TE
Jensen, M.C., Meckling, W.H.(1976). Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3, 305-360.
EP
John, T.A., John, K.(1993). Top-management compensation and capital structure. Journal of Finance, 48, 949-974.
CC
John K., Saunders, A., Senbet, L.W. (2000). A theory of bank regulation and management compensation. Review of Financial Studies, 13, 95-125.
A
John, K., Qian, Y.(2003). Incentive features in CEO compensation in the banking industry. Federal Reserve Bank of New York Economic Policy Review 9, 109–121. John, K., Mehran, H., Qian, Y.(2010). Outside monitoring and CEO compensation in the banking industry. Journal of Corporate Finance. 16, 383-399.
33
Koutsomanoli-Filippaki, A. Mamatzakis, E.(2009). Performance and Merton-type default risk of listed banks in the EU: A panel VAR approach. Journal of Banking and Finance, 33 (11). 20502061. Lambert, R. A., Larcker, D. F., Verrecchia, R. E.(1991). Portfolio considerations in valuing executive compensation. Journal of Accounting Research, 29, 129-49.
SC RI PT
Lewellen, K.(2006). Financing decisions when managers are risk averse. Journal of Financial Economics, 82, 551-589. Low, A.(2009). Managerial risk-taking behavior and equity-based compensation. Journal of Financial Economics, 92, 470-490. Pathan, S.(2009). Strong boards, CEO power and bank risk-taking. Journal of Banking and Finance, 33(7), 1340-1350.
N
U
Parrino, R., Poteshman, A. M., Weisbach, M. S.(2005). Measuring investment distortions when risk-averse managers decide whether to undertake risky projects. Financial Management, 34(1), 21-50.
M
A
Rajgopal, S., Shevlin, T.(2002).Empirical evidence on the relation between stock option compensation and risk taking, Journal of Accounting and Economics, 33(2), 145-171. Ross, S.A., Westerfield, R.W., Jaffee, J. (2010). Corporate Finance, 9th edition, McGraw-Hill.
D
Ross, S.A.(2004). Compensation, incentives, and the duality of risk aversion and riskiness. Journal of Finance, 59, 207–225.
TE
Wintoki, M.B., Linck, J. S., Netter, J. M.(2012). Endogeneity and the dynamics of internal corporate governance? Journal of Financial Economics, 105, 581-606.
A
CC
EP
Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics 126: 25-51.
34
Table 1：Descriptive Statistics of the Sample
SC RI PT
Categorized summary statistics for the variables from the 1993-2009 period are presented in Panels A through D. Panel A contains CEO related variables – compensation sensitivities (delta and vega) and their constituents, cash compensation (salary plus bonus), tenure (years of service as the CEO) and CEO’s age. All compensation structure variables are in millions of dollars. Deltas and vegas are computed with the one-year approximation method of Core and Guay (2002). Panel B contains the firm risk measures – total, systematic, and and unsystematic risks. The risk measures are computed using daily data over the fiscal year are presented as natural logs annualized variances. Similar to Low (2009), five leads and five lags of CRSP value-weighted portfolio returns are included in the market model regression to account for nonsynchronous trading. This regression is used to decompose total risk into unsystematic and systematic components. Panel C presents other firm specific control variables. Market capitalization is the natural log of the fiscal year end stock price multiplied by the company's common shares outstanding. Market to book ratio is the ratio of market value of equity to book value of equity. Book leverage ratio (in decimal) and ROA (in percent) are, respectively, total debt and net income before extraordinary items and discontinued operations, divided by total assets. Panel D presents the correlation matrix of all variables and pvalues are below the correlation coefficients.
Panel A: CEO related variables
0 0
0.020
0.054
0.168
3.816
0
0.655
0.965
1.533
15.500
3.000
6.000
11.000
42.000
53.000
57.000
61.000
80.000
Std. Dev. 2.203
Vega ($millions) Cash Compensation (Salary + Bonus, $millions)
1521
0.167
0.314
1521
1.403
1.448
CEO tenure (years)
1521
7.745
6.565
0
CEO age (years)
1521
56.959
32
Total Risk
1521
Panel B: Risk Measures 6.840 0.971 4.658
Systematic risk
1521
Unsystematic risk
1521
Market capitalization
N
6.168
6.685
7.283
11.334
1.245
2.138
4.755
5.448
6.215
9.194
6.393
0.956
4.299
5.753
6.248
6.897
11.245
Panel C: Other Firm Control Variables 1521 8025.90 19487.97 19.146 866.53 0 0 8 1521 2.123 1.133 -0.463 1.430
1958.07 0 1.919
6138.21 0 2.585
239757.83 14.3640
1521
0.913
0.031
0.556
0.903
0.918
0.929
1.012
1521
0.976
1.064
-16.195
0.844
1.122
1.374
4.315
A
CC
EP
ROA
Max 40.740
5.589
TE
Book leverage ratio
75th 0.627
A
6.372
D
Market to book ratio
Min
U
Mean 0.700
Delta ($millions)
Percentile 50th 0.246
25th 0.096
N 1521
M
Variable
35
N U SC RI PT
Panel D: Correlation Matrix of Sensitivities, Risk Measures and Control Variables
Total risk Systematic risk
0.864 <.0001 1
Unsystematic risk
Unsystematic. risk 0.960 <.0001 0.704 <.0001 1
Vega
Cash compensation
Age
-0.021 0.4233 0.017 0.5142 -0.032 0.2174 0.272 <.0001 1
-0.116 <.0001 0.011 0.6733 -0.170 <.0001 0.563 <.0001 0.291 <.0001 1
A
CC E
PT
Log(Market Cap)
Book Leverage
-0.068 0.0083 0.077 0.0027 -0.149 <.0001 1
Cash Compensation
ED
Tenure
Market to Book ratio
Delta
M
Delta
Vega
A
Systematic risk
36
Tenure
Age
0.027 0.2844 0.055 0.0334 0.016 0.5231 -0.046 0.0713 0.196 <.0001 -0.056 0.0282 1
-0.021 0.4025 -0.010 0.7078 -0.017 0.5069 0.042 0.1003 0.182 <.0001 0.075 0.0034 0.396 <.0001 1
Market capitalization -0.246 <.0001 -0.015 0.552 -0.335 <.0001 0.635 <.0001 0.281 <.0001 0.612 <.0001 -0.044 0.0846 0.037 0.1534 1
Market to book -0.163 <.0001 -0.108 <.0001 -0.164 <.0001 0.115 <.0001 0.234 <.0001 0.215 <.0001 -0.056 0.0291 -0.116 <.0001 0.284 <.0001 1
Book Leverage 0.092 0.0004 0.016 0.5285 0.128 <.0001 0.008 0.7657 -0.056 0.0299 0.075 0.0033 -0.014 0.5868 -0.083 0.0012 -0.002 0.9236 0.097 0.0001 1
ROA -0.499 <.0001 -0.399 <.0001 -0.508 <.0001 0.130 <.0001 0.173 <.0001 0.157 <.0001 -0.025 0.3228 -0.011 0.6594 0.308 <.0001 0.428 <.0001 -0.222 <.0001
N U SC RI PT
Table 2: Relationship between compensation variables and past risk variables
The table presents OLS regression of compensation structure on past risk as well as control variables. Panel A contains a regression of the compensation structure levels while Panel B contains a regression of the change in compensation structure variables on lagged risk and control variables. The columns represent the compensation variables (vega, delta, and cash compensation), and the three measures of risk. Control variables are CEO tenure, age, logarithm of market capitalization, market to book ratio, book value of leverage, and ROA. The risk variables (total, systematic and unsystematic) and control variables are one year lagged values. Year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively.
(1) 0.041*** (2.98)
Systematic riskt-1
-0.026** (-2.44)
Aget-1 Log(Market Cap)t-1
CC E
Market to Book ratiot-1 Book Leveraget-1 ROAt-1
A
Constant
-0.003** (-2.53) 0.002* (1.76) 0.145*** (31.53) -0.012* (-1.69) 0.440** (2.04) -0.000 (-0.00) -1.799*** (-7.99) Yes 1,521 0.466
Year Dummies Observations R-squared
-0.003*** (-2.94) 0.002** (2.11) 0.144*** (31.66) -0.007 (-1.08) 0.595*** (2.75) -0.009 (-1.19) -1.556*** (-7.28) Yes 1,521 0.465
PT
Tenuret-1
ED
Unsystematic riskt-1
Panel A: Dependent variable is level at time t Deltat (3) (4) (5) (6) 0.587*** (4.97) 0.206** (2.21) 0.042*** 0.585*** (3.34) (5.45) -0.003** 0.060*** 0.058*** 0.059*** (-2.56) (6.86) (6.58) (6.83) 0.002* 0.042*** 0.043*** 0.042*** (1.75) (4.65) (4.78) (4.65) 0.147*** 0.396*** 0.334*** 0.431*** (30.81) (9.97) (8.47) (10.41) -0.012* 0.387*** 0.408*** 0.388*** (-1.69) (6.46) (6.77) (6.49) 0.455** -5.417*** -4.921*** -5.179*** (2.12) (-2.91) (-2.62) (-2.80) 0.002 0.133** 0.070 0.153** (0.20) (2.00) (1.08) (2.28) -1.829*** -5.110*** -2.266 -5.469*** (-8.12) (-2.63) (-1.22) (-2.81) Yes Yes Yes Yes 1,521 1,521 1,521 1,521 0.467 0.190 0.180 0.193
A
Total riskt-1
Vegat (2)
(7) 0.406*** (6.24)
37
Cash compensationt (8)
(9)
0.284*** (5.55)
M
VARIABLES
-0.010** (-2.02) 0.017*** (3.50) 0.630*** (28.76) 0.042 (1.26) 1.806* (1.76) -0.045 (-1.24) -8.773*** (-8.18) Yes 1,521 0.431
-0.010** (-2.12) 0.017*** (3.51) 0.577*** (26.65) 0.046 (1.40) 1.724* (1.67) -0.073** (-2.03) -6.965*** (-6.82) Yes 1,521 0.428
0.277*** (4.65) -0.011** (-2.21) 0.018*** (3.59) 0.636*** (27.71) 0.050 (1.50) 2.162** (2.10) -0.055 (-1.48) -8.272*** (-7.65) Yes 1,521 0.424
Systematic risk t-1 Unsystematic risk t-1
Log(MV) t-1 Market to Book ratio t-1 Book Leverage t-1 ROA t-1
CC E
Constant
ED
Age t-1
-0.000 (-0.62) -0.001 (-1.21) 0.012*** (3.23) 0.010** (2.02) -0.186 (-1.11) -0.004 (-0.53) 0.029 (0.17) Yes 1,274 0.071
PT
Tenure t-1
A
Year Dummies Observations R-squared
N U SC RI PT
(1) 0.020* (1.81)
A
Total risk t-1
Panel B: Dependent variable is change from t to t-1 Vega) t Delta) t (2) (3) (4) (5) (6) 0.189*** (4.64) 0.007 0.156*** (0.86) (5.09) 0.011 0.152*** (1.08) (4.00) 0.000 -0.001 0.004 0.004 0.004 (0.28) (-0.70) (1.40) (1.46) (1.25) 0.001 -0.001 0.003 0.003 0.003 (0.82) (-1.16) (1.02) (0.92) (1.10) 0.009** 0.012*** 0.029** 0.001 0.034** (2.49) (3.01) (2.11) (0.08) (2.40) 0.013** 0.011** 0.087*** 0.086*** 0.090*** (2.43) (2.14) (4.50) (4.49) (4.65) -0.020 -0.169 -1.123* -1.272** -0.997 (-0.11) (-1.01) (-1.80) (-2.04) (-1.60) 0.000 -0.004 0.064*** 0.058** 0.064*** (0.03) (-0.62) (2.60) (2.37) (2.59) -0.128 -0.019 -0.462 0.311 -0.718 (-0.73) (-0.11) (-0.71) (0.51) (-1.11) Yes Yes Yes Yes Yes 1,274 1,274 1,274 1,274 1,274 0.069 0.070 0.121 0.124 0.117
M
VARIABLES
38
Cash compensation) t (7) (8) (9)
0.156** (2.43) 0.164*** (3.41)
-0.003 (-0.66) -0.003 (-0.70) -0.016 (-0.76) -0.008 (-0.27) -0.048 (-0.05) -0.034 (-0.87) -0.235 (-0.23)
-0.003 (-0.56) -0.004 (-0.81) -0.041** (-2.00) -0.011 (-0.38) -0.261 (-0.27) -0.036 (-0.94) 0.354 (0.37)
0.114* (1.92) -0.003 (-0.74) -0.003 (-0.65) -0.013 (-0.59) -0.005 (-0.17) 0.064 (0.07) -0.035 (-0.89) -1.225 (-1.21)
Yes 1,274 0.086
Yes 1,274 0.091
Yes 1,274 0.085
N U SC RI PT
Table 3: Risk persistence over time
The table presents OLS regression of risk levels on past risk levels, as well as control variables to establish risk persistence. The columns represent the risk variables (total, systematic and unsystematic). Control variables are CEO tenure, age, logarithm of market capitalization, market to book ratio, book value of leverage, and ROA. Year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively. Total Risk t VARIABLES risk t-1
M
risk t-3
Age t
PT
Log(MV) t
ED
risk t-4 Tenure t
CC E
Market to Book ratio t Book Leverage t
A
ROA t
Intercept
Year Dummies Observations R-squared
(2)
A
risk t-2
(1) 0.622*** (15.73) 0.063 (1.35) 0.016 (0.34) -0.020 (-0.48) 0.000 (0.25) -0.001 (-0.42) 0.001 (0.13) 0.020 (1.29) 1.825*** (3.24) -0.137*** (-8.63) 0.275 (0.47) Yes 716 0.923
Systematic Risk t (3) (4) 0.453*** (12.65) 0.122*** (3.34) 0.007 0.206*** (0.20) (5.82) -0.003 0.099*** (-0.08) (2.83) -0.001 -0.005* (-0.33) (-1.73) -0.003 -0.001 (-1.01) (-0.31) 0.019* 0.013 (1.69) (1.03) 0.039** 0.073*** (2.14) (3.51) 0.862 0.318 (1.27) (0.42) -0.101*** -0.135*** (-5.44) (-6.30) 1.103* 3.461*** (1.70) (4.71) Yes Yes 716 748 0.904 0.864
0.293*** (6.00) 0.106** (2.20) -0.001 (-0.61) -0.001 (-0.21) -0.008 (-0.67) 0.049*** (2.65) 1.010 (1.51) -0.205*** (-10.79) 5.579*** (8.18) Yes 748 0.877
39
Unsystematic Risk t (5) (6) 0.596*** (14.48) 0.060 (1.22) 0.080* 0.333*** (1.66) (6.58) -0.020 0.120** (-0.47) (2.42) 0.002 0.001 (0.82) (0.30) -0.000 -0.001 (-0.08) (-0.45) -0.005 -0.024* (-0.45) (-1.77) 0.014 0.042** (0.78) (2.04) 1.958*** 0.895 (2.98) (1.19) -0.168*** -0.251*** (-9.01) (-11.70) -0.144 2.030** (-0.21) (2.52) Yes Yes 716 748 0.898 0.848
N U SC RI PT
Table 4: The relationship between risk and lagged values of compensation variables for all banks (SIC Code = 6020, 6035, and 6036) This table reports the dynamic panel GMM estimation of the model, along with other models, as follows:
Risk i ,t 0 1 Risk i ,t 1 2 Risk i ,t 2 1Vega i ,t 1 2 Delta i ,t 1 3 CashCompensation i ,t 1 ControlVar aibles i ,t YearDummies i i ,t
Total Risk t
(-8.76) 0.053***
(-4.96) 0.010
(-1.13) 0.012
(-0.14) -0.030
(4.72) 0.062***
(-0.60) 0.016
(3.24) 0.030**
(2.64) -0.009
(-12.84) 0.049***
(-6.08) 0.004
(-2.80) 0.004
(-0.92) -0.035
Leverage t
(3.92) 1.932***
(0.57) -1.178
(1.00) 1.717***
(-1.01) 2.470***
(3.63) 2.742***
(0.73) -0.216
(1.97) 1.561***
(-0.25) 2.791**
(3.29) 1.701***
(0.20) -1.709*
(0.29) 1.788***
(-1.04) 2.233***
(4.16) -0.150*** (-10.64)
(-1.35) -0.101*** (-6.68)
(-0.20) -0.078*** (-4.13)
(2.78) -0.091*** (-6.24) 0.479*** (15.77) 0.109*** (3.77) 1.789***
(2.18) -0.071** (-2.36) 0.366** (2.47) 0.139 (1.16) 1.160
(3.31) -0.183*** (-11.73)
(-1.75) -0.126*** (-7.45)
8.794***
(2.93) -0.078*** (-3.58) 0.626*** (4.26) -0.043 (-0.24) 1.396
(4.69) -0.116*** (-6.54)
5.599***
(3.96) -0.112*** (-9.71) 0.637*** (19.58) 0.010 (0.32) 0.741
6.031***
9.377***
(3.61) -0.132*** (-10.02) 0.615*** (18.67) 0.037 (1.10) 1.388**
(2.85) -0.094*** (-3.85) 0.637*** (4.90) -0.139 (-0.48) 2.102
Tenure t
A
Log(MV) t
CC E
Age t
ROA t
ED
Cash comp/1000 t-1
risk t-1 risk t-2 Constant
(4) GMM 0.186 (1.42) 0.029*** (4.30) -95.626* (-1.92) 0.000 (0.11) 0.000 (0.04) -0.005
(5) OLS -0.318*** (-4.69) 0.014* (1.74) 57.854*** (4.11) -0.009*** (-3.50) 0.005** (1.96) 0.074***
(6) FE -0.448*** (-6.03) -0.021** (-2.03) -54.161*** (-3.35) -0.001 (-0.30) 0.006 (1.44) -0.028
(7) DOLS -0.097* (-1.66) 0.008 (1.25) -0.725 (-0.05) -0.002 (-0.68) -0.000 (-0.16) 0.045***
(8) GMM 0.007 (0.04) 0.028*** (3.58) -138.130* (-1.76) -0.001 (-0.34) -0.000 (-0.09) 0.095***
(9) OLS 0.101* (1.70) 0.032*** (4.42) 45.981*** (3.71) -0.005** (-2.17) 0.002 (0.73) -0.178***
(10) FE -0.041 (-0.62) 0.003 (0.29) -19.307 (-1.34) -0.004 (-0.97) 0.008** (2.19) -0.256***
(11) DOLS 0.050 (0.98) 0.015** (2.47) 11.136 (0.97) -0.000 (-0.00) -0.000 (-0.07) -0.039***
(12) GMM 0.311* (1.74) 0.033*** (3.24) -96.319* (-1.66) 0.000 (0.04) 0.001 (0.20) -0.065
M
Market/Book t
Delta t-1
(2) FE -0.110* (-1.86) -0.003 (-0.31) -28.114** (-2.18) -0.005 (-1.38) 0.008** (2.36) -0.187***
Unsystematic Risk t
(3) DOLS 0.013 (0.29) 0.013** (2.51) 6.950 (0.68) -0.001 (-0.39) -0.000 (-0.20) -0.013
Vega t-1
(1) OLS 0.024 (0.44) 0.025*** (3.88) 49.981*** (4.46) -0.006*** (-3.00) 0.002 (1.09) -0.109***
Systematic Risk t
PT
VARIABLES
A
The columns represent the dependent variables – unsystematic, systematic, and total risks, and the four models, OLS, fixed-effects (FE), dynamic OLS (DOLS) and GMM. Compensation structure variables (Vega, Delta and cash compensation) are lagged one year. Control variables are CEO tenure, age, logarithm of market capitalization, market to book ratio, book value of leverage, and ROA. All the dynamic GMM models are based on 1058 observations from 15 years (1995 – 2009). 14 year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively. In GMM estimation, for first-differenced equations, the GMM instruments include the lagged vega, delta, and cash compensation from 3 years and further. For level equations, the GMM instruments again include the lagged differences of vega, delta and cash compensation from 2 years ago and further. AR(1) and AR(2) p-values are for tests of first and second-order serial correlation in the first-differenced residuals with the null of no serial correlation. Hansen’s J-statistic p-values are for over-identification test of the instruments in the differenced equations under the null that instruments are valid. The Diff-inHansen test p-values are for exogeneity of the instruments in the level equations with the null that all instruments are exogenous.
1.892***
5.661*** 40
(1.55) Yes 1,058 0.906
(0.89) Yes 1,058
0.00, 0.25 0.188 0.887
N U SC RI PT
(9.00) Yes 1,274 0.908
(3.22) Yes 1,274 0.828
(4.62) Yes 1,274 0.906
A
CC E
PT
ED
M
A
Year Dummies Observations R-squared AR(1)/AR(2) (p-value) Hansen’s J-stat (p-value) Diff-in-Hansen test (p-value)
(12.00) Yes 1,274 0.832
41
(3.21) Yes 1,058 0.890
(0.98) Yes 1,058
(11.68) Yes 1,274 0.788
(8.59) Yes 1,274 0.881
(2.55) Yes 1,058 0.875
(0.78) Yes 1,058
0.01, 0.91
0.00, 0.26
0.227
0.187
0.290
0.271
Table 5. The influence of commercial bank, large bank and bank with high leverage
SC RI PT
In this table, we report the dynamic panel GMM estimation results of the risk model with interaction terms between CEO compensation (Vega and Delta) and bank characteristics (dummies for commercial bank, large bank and bank with high leverage). Total risk, systematic risk and unsystematic risk are dependent variables in columns (1)-(3), respectively. Dummy variables SIC6020, LARGE, HIGHLEV are equal to one if the bank belongs to commercial bank, and bank-year observation has values above the median in bank size and book leverage ratio in the year, otherwise zero. vegat-1*SIC6020, vegat-1*LARGE, and vegat-1*HIGHLEV are interaction terms between lagged vega and the dummies for commercial bank, large bank and bank with high leverage ratio respectively. delta t-1*SIC6020, deltat-1*LARGE, and deltat-1*HIGHLEV are interaction terms between lagged delta and the dummies for commercial bank, large bank and bank with high leverage ratio respectively. In GMM estimation, for first-differenced equations, the GMM instruments include the lagged variables of vega, delta, and cash compensation from 3 years ago and further. For level equations, the GMM instruments include the lagged differences of vega, delta and cash compensation from 2 years ago and further. AR(1) and AR(2) p-values are for tests of first and second-order serial correlation in the residuals with the null of no serial correlation. Hansen’s J-statistic p-values are for overidentification test of the instruments in the differenced equations under the null that instruments are valid. The Diff-in-Hansen test pvalues are for exogeneity of the instruments in the level equations with the null that all instruments are exogenous. Year dummies are included. ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent level, respectively. Dynamic GMM with Interactions of Commercial Bank, Large Bank and High Leverage Total Riskt Systematic Riskt Unsystematic Riskt (1) (2) (3) vega t-1 -0.284 -4.495 -2.385 (-0.07) (-1.39) (-0.40) vega t-1*SIC6020 -0.427 1.682 -0.447 (-0.20) (0.95) (-0.19) vega t-1*LARGE 0.626 2.280 2.744 (0.25) (0.91) (0.63) vega t-1*HIGHLEV 0.517 0.938** 0.623 (1.25) (2.44) (1.24) delta t-1 0.721 1.250* 1.309 (1.01) (1.84) (1.40) delta t-1*SIC6020 -0.490* -0.423** -0.743** (-1.85) (-2.01) (-2.12) delta t-1*LARGE -0.230 -0.826 -0.557 (-0.47) (-1.46) (-0.85) delta t-1*HIGHLEV -0.327 -0.299* -0.526** (-1.54) (-1.74) (-2.07) (Cash comp/1000) t-1 -66.982 -63.472 -49.530 (-1.16) (-0.95) (-0.83) tenure t -0.005 -0.008 -0.006 (-0.81) (-1.17) (-0.69) Age t -0.000 0.001 0.002 (-0.01) (0.21) (0.35) Log(MV) t 0.022 0.138*** -0.006 (0.52) (3.29) (-0.07) Market/Book t -0.023 -0.003 -0.018 (-0.68) (-0.07) (-0.44) Leverage t 2.860** 2.498** 3.206** (2.45) (2.10) (2.33) ROA t -0.078*** -0.078** -0.091*** (-2.98) (-2.04) (-2.97) risk t-1 0.564*** 0.236* 0.580*** (4.06) (1.74) (3.82) risk t-2 0.106 0.096 0.067 (0.46) (0.72) (0.21) Constant 0.000 0.000 -0.731 (.) (.) (-0.20) Year Dummies Yes Yes Yes Observations 1,058 1,058 1,058 AR(1)/AR(2) (p-value) 0.00, 0.77 0.01, 0.80 0.00, 0.87 Hansen’s J-stat (p-value) 0.093 0.141 0.160 Diff-in-Hansen test (p-value) 0.564 0.175 0.696 (p-value) 42
A
CC
EP
TE
D
M
A
N
U
VARIABLES