The effectiveness of strong governance and risk
oversight on the mitigation of tail risk exposure
Jordy Kamphorst
†June 6, 2018
Abstract
I use U.S. Bank Holding Companies’ (BHCs’) board structure and risk oversight embed-dedness characteristics to construct a Governance Strength Index (GSI) which proxies for the strength of the governance at the BHC. Over the time-period 2006-2014, I show that BHCs which had a stronger governance framework in place, had a substantial lower tail risk expo-sure. To measure tail risk, which is defined as a BHC’s one-day expected shortfall (ES) for a specific year, I use the class of threshold exceedance models within Extreme Value Theory (EVT). By means of Maximum Likelihood Estimation (MLE), I fit the stock return data of the BHC to a Generalized Pareto Distribution to establish the BHC’s one-day ES. Given the model’s stringent assumptions on the behavior of the stock return data, I show that the results are robust when I use other models to measure risk exposure and other ways to mea-sure the governance strength of the BHC. The use of a dynamic panel Generalized Method of Moments-estimator (GMM) provides evidence that the results are not driven by potential endogeneity between governance strength and tail risk. Robustness of the results is further supported by bootstrapping, a GLS-RE estimator and a first-differenced (FD) model. This research therefore implies that a strong governance within U.S. BHCs seems to mitigate their exposure towards tail risk.
† Student number: 3262707. Supervisor: Prof. Dr. K.F. Roszbach. I am grateful for the feedback I have received
Contents
1 Introduction 3
2 Literature review 5
2.1 Corporate governance and risk oversight . . . 5
2.2 Risk and tail risk exposure . . . 7
2.3 Strong governance and risk taking . . . 10
2.4 Hypotheses . . . 11
3 Data 13 3.1 Measurement of tail risk exposure . . . 13
3.2 Alternative measures of risk . . . 15
3.3 Measurement of strong governance and risk oversight (GSI) . . . 16
3.4 Alternative measures of strong governance . . . 17
3.5 Control variables . . . 18
3.6 Descriptive statistics . . . 19
4 Methodology 22 4.1 Panel-data framework . . . 22
4.2 Addressing endogeneity: dynamic panel GMM-estimator . . . 23
4.3 Robustness checks . . . 24
5 Empirical results and analysis 25 5.1 Panel framework - structural differences in BHCs’ GSI . . . 25
5.2 Panel framework - relationship GSI and tail risk exposure . . . 28
5.3 Panel framework - relationship alternative GSI and tail risk exposure . . . 30
5.4 Panel framework - relationship GSI and alternative risk metrics . . . 32
5.5 Dynamic panel GMM-estimator - addressing endogeneity . . . 34
5.6 Robustness checks . . . 36
6 Conclusion 37
References 39
1
Introduction
The ‘traditional’ view on a bank’s role within society is an intermediary one in which they take deposits and provide loans (Kashyap, Rajan and Stein, 2002). However, over time, a substantial increase in the complexity of a bank’s assets, liabilities and activities fueled by a rapidly expanding derivative market and (de)regulation have dramatically changed the scope and impact of banking. While the bank’s traditional role is still prominent, these changes have increased the complexity of managing and mitigating their risks substantially. The widened scope of the bank’s activities, in that perspective, also further enhanced the conflicting interests that might arise.
One could, from a theoretical perspective, argue why banks would engage in actively managing and mitigating their risks. Under certain assumptions, Modigliani and Miller (1958) propose that firms should not engage in such activities. That is because investors can more effectively eliminate a firm’s idiosyncratic risk by holding a well-diversified portfolio and therefore do not value these activities. Under this theorem, banks would be redundant and in essence non-existent, which is inconsistent with reality. The theorem makes assumptions regarding markets, which are not met in reality and therefore distort the propositions made by the Modigliani and Miller-theorem
(Diamond 1984; Aghion and Bolton, 1992; Hart, 1995). For instance, banks trade in assets
which are information-intensive in nature and can therefore not be traded frictionless in markets;
something which the Modigliani and Miller-theorem assumes. At the same time, the bank’s
maturity transformation imposes challenges from a risk management perspective; Froot and Stein (1998) show that value-maximizing banks do have a real concern with proper risk management and oversight. Related models show congruent results (Kashyap and Stein, 1995), thereby providing evidence for a departure from the neoclassical framework of Modigliani and Miller.
The recent financial crisis has shown us that inadequately mitigating the risks that are inherent to a bank, can have profound consequences. The low interest environment, the use of short-term funding and the high interdependency of banks on complexly structured assets, worked like a toxic substance. The aggravating consequences of the subsequent ‘fire sales’ of those assets (Shleifer and Vishny, 2011) made systemic risk, with potential devastating effects for the real economy, a threat (Brunnermeier, 2009). Banks either intentionally kept the risk on their books and in essence willingly took substantial tail risk, thereby neglecting and suppressing risk management (Kashyap, Rajan and Stein, 2008), or management was unable to foresee the seemingly low-probability risks that ultimately proved to be very significant (Ellul and Yerramilli, 2013). As noted by Faleye and Karthik (2017), one of the most prominent reasons is that banks intentionally kept the risk on their books and a weak governance framework might be at the foundation of this behavior. Indeed, risk oversight is embedded in the overall governance framework of banks and can only be effective when this framework is well-established.
have partly driven the cross-sectionally observed differences on tail risk exposure. This therefore raises the question whether a strong governance did indeed mitigate excessive risk taking by banks during this period, but also in the years subsequent to it.
Based on this, I hypothesize that BHCs with a stronger governance framework had a lower tail risk exposure over the period 2006-2014. I thoroughly address this question by using a sample of 53 U.S. BHCs. I obtain their, academically supported, governance and risk oversight characteristics and create a Governance Strength Index (GSI) which proxies for the overall governance strength at the BHC. The GSI is based on the first principle component out of a principle component analysis
on the governance characteristics. This method is based on the work of Ellul and Yeramilli
(2013). To my knowledge, no other empirical work has manually collected such an extensive coverage of governance and risk oversight characteristics. I use a risk model and proxy based on market data and thereby follow, amongst others, Wagner and Knaup (2012), Ellul and Yeramilli (2013), and Laeven and Levine (2009). Assuming market participants have in aggregate a rational perception on the BHC’s value and risk, market data should provide a valuable signal on the BHC’s inherent risk exposure. The model used is one from the field of extremes and risk modeling to measure the BHCs’ tail risk exposure. This model is a threshold exceedance model within Extreme Value Theory (EVT) to fit empirical return data of the BHC’s stock to a Generalized Pareto Distribution by means of Maximum Likelihood Estimation (MLE). This is to come up with the one-day Expected Shortfall (ES) which is a proxy for tail risk exposure.
to the corporate finance and banking literature by showing that a BHC’s governance strength is, through its monitoring and advisory role, value-enhancing in that it mitigates the bank’s tail risk exposure.
The remainder of this study is structured as follows: section two provides a discussion on the relevant literature and states this study’s hypotheses. Section three delves deeper into the details of the data and the measurement of variables. Section four amplifies on the applied methodology. Section five provides the empirical results and analysis of this study. This study is finalized in section six by means of a conclusion and discussion of the empirical results and their implications.
2
Literature review
2.1
Corporate governance and risk oversight
According to the agency theory, firms are owned by principles which delegate operational and financial decisions to agents which should aim to maximize the firm’s value and provide principles with a return on their investment. Yet, the incentives and motives of agents are not necessarily aligned with those of the principle; a non-optimal situation might arise in which agents expropriate funds put up by principles (Shleifer and Vishney, 1997). Contracting can, in theory, solve these problems. However, the future is unknown, new information accrues and circumstances that were not clearly conceptualized at initiation arise, which cannot be contracted upon. Contingent control contracts as proposed by Kaplan and Strömberg (2003) might mitigate some of the encountered problems but leaves agents with plenty discretionary control in other areas to expropriate funds. Another way to steer principles off non-value maximizing behavior is by passive market monitoring (Holström and Tirole, 1993) or by actively appointing a monitor (Tirole, 2006) which oversees the agent’s activities. Without delving too deep in agency and contracting theory, corporate governance is concerned with these very real issues. Given the several definitions for corporate governance that exist, one which seems to capture the essence is provided by Andres and Vallelado (2008). They define corporate governance as a group of mechanisms used by stakeholders to ensure that directors efficiently manage corporate resources, a task that includes the manner in which quasi-rents are developed and distributed. This definition closely matches the one provided by Shleifer and Vishney (1997) and touches well on the issues as opted by the agency theory.
been criticized on whether the mandates had any empirical effect (Romano, 2005). The recent financial crisis has fueled the discussion on the effectiveness of governance in banks and its role in providing financial stability (Berger, Imbierowicz and Rauch, 2016). While this provided ample legislation for banks and their governance framework, such as the Federal Reserve’s Enhanced Prudential Standards, it remains questionable whether these regulations had their desired effects. Adams and Mehran (2012) additionally note that U.S. BHCs are different from regular publicly listed companies in that they are holding companies. Directors of the BHC often sit on the board of the group’s lead-bank, making them subject to bank-level regulatory restrictions. Depending on whether this is a national bank or a state bank makes them subject to different legislation. For instance, state-level legislation might require board members to hold a certain percentage of shares, thereby influencing the BHC’s governance strength.
The literature provides a substantial amount of characteristics which can contribute to a bank having a ‘strong’ governance framework; often arguments against these characteristics can be presented. I will touch upon the most prominent academically supported characteristics and their potential theoretical counterarguments. I will refrain myself from discussing standardized indexes as for instance applied by Ferreira and Laux (2007); the lack of flexibility that is inherent to such indexes make these inferior to a manual designed metric.
As argued by Kashyap, Rajan and stein (2008), a strong and independent board is at the foun-dation of having a strong governance framework. Optimally, these boards have a composition that is well-balanced with respect to monitoring and advisory capabilities (Andres and Vallelado, 2008; Adams and Mehran, 2012). The independence of board members gives rise to a potential increase in the valuableness of their advisory and monitoring tasks. However, given the lack of firm-specific knowledge induced by independence, this might give rise to difficulties (Adams and Ferreira, 2007). Potentially more troubling, Adams and Merhan (2012) note that directors are often customers of the bank, which might provide different motives and incentives than those that would expected from completely independent directors. This mere observation gives rise to a feculent image of independence which might bias results. To overcome this problem they proxy for board strength with the fraction of outside directors as well as the fraction of non-insiders. Nonetheless, board independence seems to be a characteristic which clearly contributes to a stronger governance framework.
The frequency of board meetings can be seen as another attribute which contributes towards having a stronger governance framework (Andres and Vallelado, 2008). More frequent meetings enable the possibility to exchange ideas and to execute monitoring and advisory tasks. Unfortunately, the frequency might also be a reactive measure due to poor performance. Another attribute which might contribute, but which is flawed with counterarguments, is the size of the board. While a larger board enhances the possibilities of monitoring and advising, problems in the field of decision making, coordination and control arise (Andres and Vallelado, 2008). Therefore, both characteristics fail to distinguish themselves as characteristics which clearly contribute towards a stronger governance framework.
of CEO and chairman are not separated, the CEO’s personal interests are likely influencing the decisions process, which makes the board’s monitoring and advising role potentially weaker. It can therefore be argued that the separation of CEO and board chairman is a characteristic that contributes towards a stronger governance framework. The number of board committees (Adams and Merhan, 2012), is found to be another important determinant, but then in the context of BHC performance.
Ellul and Yerramilli (2013) note that, to have risk oversight properly embedded in the BHC, a Chief Risk Officer should be appointed which ideally is also an executive officer. In this way, one person at the senior level is solely responsible for risk oversight and can effectively communicate on such matters at the board and management level. A further indicator that risk oversight is given a relative prominent place within the BHC is whether the CRO is among the top five highest paid executives. It is furthermore argued that a board committee should be in place, which is entitled to review the risk management procedures and the BHCs risk exposure. Such a committee provides a further ’line of defense’ in overseeing risk and acting adequate to it. As is further argued by Ellul and Yerramilli (2013), it is desirable to have an independent director with prior industry experience in this committee. Banks are exposed to different kinds of risk than regular firms and as such an independent director with prior industry experience is better able to make judicial choices in this field.
The main insight obtained from this section is that corporate governance stems from the agency problem. Until the financial crisis, a relative minor body of literature and legislation has dealt with governance within banks; something which due to its opaqueness would have been expected. The corporate goverance literature argues that having more independent directors, a separate board chairman, more board committees, having a CRO which ideally is an executive and is an important executive as proxied by its relative pay and having a risk committee which has industry experience all contribute towards a stronger governance framework. Other characteristics, as argued, might contribute as well, but are flawed by counterarguments and as such are less desirable to use.
2.2
Risk and tail risk exposure
Banks are exposed to a wide-variety of risks. The major risks they are exposed to include credit, market and operational risk. For these type of risks banks have to hold regulatory capital under the Basel framework. Another important source of risk, which proved to be important during the financial crisis when liquidity dried up, is liquidity risk. Banks can use a wide-variety of ‘channels’ to leverage their exposure to variables. For instance, it is well-documented that the U.S. monetary policy, in particular the relative low-interest environment between 2002 and 2004, induced excessive risk taking and leveraging by banks. These factors fueled the substantial increase in asset prices, which ultimately imploded (Dell’Ariccia, Laeven and Suarez, 2017).
reduce credit and liquidity risk. Vazquez and Federico (2015) note that the excessive risks taken by banks were not commensurate with their liquidity and capital buffers. Two arguments made many academics argue for an approach at the macro-level to safeguard financial stability and to mitigate systemic risk, rather than a micro-based-approach as set by Basel III (Vazquez and Federico, 2015). The first is the observation on the existence of a high interdependency of banks that arose from direct contractual links and heightened credit risks of counterparties. The second being a direct effect via prices and liquidity spirals (Brunnermeier, 2009).
For banks, quantifying and measuring their risk is, as argued in section 1, important; several models and methods exist to measure their risk exposure on a portfolio-, division- or bank-level. However, these models and methods vary substantially in practical applicability and technical sophistication. In the academic field, one can distinguish between measuring bank-level risk based on accounting data, as for instance done by Laeven and Levine (2009), and Bhagat, Bolton and Lu (2015), and one focused on using market-based data (Wagner and Knaup, 2009; De Jonghe, 2009; Ellul and Yeramilli, 2013). The market-based approach is an appealing one. Assuming market participants have in aggregate a rational perception on the BHC’s value and risk, this should provide a valuable signal on the BHCs inherent risk exposure. Often, studies use both accounting- and market-based risk proxies as robustness (Laeven and Levine, 2009).
In the academic field, risk proxies for bank-level risk are often based on models from the field or credit risk. One well-known model, which is based on accounting data, is aimed at estimating a firm’s insolvency likelihood. This model is the Z-Score (Altman, 1968). Modifications of the Z-score exist which better fit in the context of banks. The Z-score as risk proxy is applied by, amongst others, Laeven and Levine (2009), and Bhagat, Bolton and Lu (2015). These studies define the Z-score as the return on assets plus the equity to asset ratio divided by the standard deviation of these assets’ returns. The higher the Z-score, the further away the bank is from insolvency, and therefore, as argued, has less inherent risk. Although the Z-score is widely used in the academic literature, it is based on accounting data. As argued by Laeven and Levine (2009), this makes the Z-score backward-looking. Therefore, when available, models based on market data are favored. Other accounting-based risk proxies are often financial ratios. One ratio that is a rather natural candidate, that the academic literature often uses, is the ratio of impaired loans to asset or tier-1 capital (Ellul and Yeramilli, 2013). A bank that has a high value on the latter ratio is an indicator that the bank is mores prone to solvency risk. This therefore makes the bank more vulnerable to bankruptcy or capital restructuring.
and the bank defaults. Based on this argumentation, a modification of the Black-Scholes-Merton model can be used. By using some results within stochastic calculus one can ultimately derive the bank’s probability of default, which can be used as a risk proxy. Although appealing, the Merton model is too restrictive to be used in this context.
More recently, academic literature acknowledged that other market-based proxies which are based on the stock returns of the bank provide another compelling way to look at risk exposure (Laeven and Levine, 2009; Ellul and Yeramilli, 2013). For instance, by estimating the volatility of the stock’s return and use this as a proxy for risk (Laeven and Levine, 2009). In that perspective, the risk management literature and the Basel framework have lately focused more on the occurrence and modeling of extreme realizations of market variables. The extreme variable realizations occur rarely and are therefore at the far ends of the variable’s distribution. However, when they do occur they have potential devastating effects. A study focused on these tail realizations within banks, is the study by Ellul and Yerramilli (2013). They proxy for bank-level risk by defining an ES on the BHC’s stock return, which quantifies the severity of these tail realizations. The notion of tail comes from an underlying probability distribution of a variable. Let (Ω , F , P) be a probability space which describes the probability P, that a certain realization out of the possible set of realizations F , will occur at some future time. Tails refer to the realizations that have attained an extremely low probability to be encountered. When modeling the tail of a variable’s distribution, empirical data often lacks enough observations to make tail smoothing and extrapolation possible. It is therefore sometimes assumed that the underlying distribution is normal. As noted by De Jonghe (2009), the assumptions of a normal distribution might be rational when one wants to obtain central dependency measures. However, given the evidence that marginal distributions are not normally distributed, especially in the tails, this distribution lacks sophistication in determining actual tail realizations. This makes risk proxies based on these tails severely flawed. One can measure the tails of the distribution and consequently the probability of tail event realizations more accurately, while being able to smooth the tail and extrapolate, by applying a model within Extreme Value Theory (EVT). Within EVT the class of threshold exceedance models is often used. These models are based on the observation that the empirical tail distribution converges to a Generalized Pareto Distribution (GPD). This model thus overcomes the flaws of the normal distribution on the one hand, but on the other hand overcomes the lack of empirical observations to smooth and extrapolate. This model can then be used to measure ES as a risk proxy, which not only incorporates the empirical tail realizations, but also extrapolates beyond them (McNeil et al., 2005).
2.3
Strong governance and risk taking
The literature provides me with empirical findings which can provide further insight in the relation of corporate governance and risk within a banking context. In the corporate governance and banking literature, studies have used bank characteristics, the competitive environment, economic conditions or monetary policy to measure their impact on the risk exposure or performance of the bank. These studies have also aimed to establish confidence in the way causality runs; the corporate governance literature is plagued by potential endogenity (Wintoki et al., 2012). While the mere complexity of a bank and its economic environment make it impossible to determine a fixed set of factors which consistently can explain the risk that they take, acquiring and establishing factors that significantly influence the bank’s risk exposure provides ample insight for regulators. In recent papers by Adams and Mehran (2012), and Faleye and Krishnan (2017), it is noted that a relatively minor body of studies has focused on the role of corporate governance in banks. However, as noted by Faleye and Krishnan (2017) and Ellul and Yerramilli (2013), there is a believe that the excessive risks taken and the cross-sectionally observed differences on a bank’s exposure were, amongst other reasons, to be blamed on the governance framework of the bank. This strengthens the belief that corporate governance and risk taking are related.
Adams and Mehran (2012) argue, by using a sample of U.S. BHCs tracked over 34 years, that banks did not necessarily choose ineffective boards, but provide evidence that BHCs which have a larger board of directors perform better, as measured by Tobin’s Q. They thereby argue that larger boards have more directors with subsidiary directorships and these directors may be better suited to deal with organizational complexity. These findings are somewhat in conflict with Andres and Vallelado (2008), they find an inverse U-shaped relation between board size and performance, noting that a larger yet not excessively large independent board can effectively fulfill its advising and monitoring tasks.
risk management position, leads to lower tail risk. They define tail risk as the five percent lowest returns on the BHC’s stock in a year. They also establish confidence in the way causality runs by addressing endogeneity via Two-Stage Least Squares and a GMM-estimator.
The main insight obtained from this section is that a relative minor body of literature has fo-cused on the impact of overall governance strength on risk exposure within a banking context. A well-known issue in these studies is endogeneity, which one should deal with properly. The literature that is available, however, is focused on a few characteristics of governance; not the wider governance framework. Moreover, these studies often use rather simple measures of risk, or those which can be improved upon. Therefore, there remains a gap in the literature in which the impact of the overall governance framework on tail risk exposure is measured. Moreover, their remains room for risk proxies which more thoroughly use data to model the inherent risk that is further in the tails.
2.4
Hypotheses
The main insight provided by the last subsection, is that a relative minor body of literature exists that investigates the impact of the corporate governance of a bank on its (tail) risk exposure.
However, after the financial crisis there has been an increased interest in this subject. This
increased interest is largely driven by the public and academic believe that much of the excessive risk taken can be partly attributed towards the lack of an effective governance framework at banks (Faleye and Krishnan, 2017). Still, there remains a gap in the literature. No research has fully amalgamated a wider range of different characteristics which determine the strength of the governance framework at a bank and related it to the impact it has on tail risk exposure. The study by Ellul and Yerramilli (2013) partly fills the gap. However, they have a different approach in measuring tail risk and have a sole focus on the impact of the risk management function in it. As argued earlier, risk oversight can only function properly when the complete governance framework is efficiently structured. This study tries to fill this gap by using a comprehensive measure of governance strength which includes both characteristics related to the governance framework and risk oversight. Moreover, this study uses a more sophisticated model as a basis for the bank’s risk proxy. In subsections 3.3 and 3.1, I delve deeper in how I am measuring these components. Based on this discussion and the insight obtained from the literature review, my main hypothesis is as follows:
H1: U.S. BHCs that had a stronger governance and risk oversight framework in place,
had a lower tail risk exposure during the 2006-2014 period.
channel it is argued that the risk culture might determine the extent of risk taken and that the governance framework might be designed to accommodate this risk culture. The hedging channel argumentation follows from the belief that banks that are currently experiencing or are going to experience more significant amounts of risks, are likely to put up a stronger governance framework in place to ‘hedge’ these risks. I already accommodate and test for potential endogeneity when I address my main hypothesis. However, if the hedging argumentation channel would hold, one would expect that banks which experienced significant tail risk during the financial crisis (2008 and 2009) increased the strength of their governance structure in the subsequent years; more than those who experienced lower amounts of risk. However, if the business model channel would hold, one would likely not observe BHCs which experienced more risk to increase their governance strength more than those who did not. Based on this discussion my second hypothesis follows:
H2: U.S. BHCs that had a larger than median tail risk exposure during 2008-2009,
improved their level of governance and risk oversight strength more than those who did not have a larger than median tail risk exposure.
The last hypothesis is somewhat related to regulation and policy effectiveness. Given the substan-tial increase in legislation and larger scrutiny on banks, one would expect that the overall level of governance strength within BHCs increased in the years after the financial crisis. Note that this hypothesis depends greatly on the two other hypotheses in terms of interpretation. There can be a variety or reasons why BHCs improved their governance framework. One is the possible endogenous interaction of the high risks during the financial crisis and the choice for the level of governance strength afterwards. However, if I can rule out that this potential endogenous interac-tion is driving the results I find under the main hypotheses, then the improvements are most likely driven by enhanced legislation and more supervisory scrutiny. Ultimately, the third hypothesis follows:
H3: The strength of the governance and risk oversight framework in U.S. Bank
Hold-ing Companies has increased in the years subsequent of the financial crisis.
3
Data
This section will delve deeper into the variables that this study uses to answer the stated hy-potheses. The data section has been deliberately put in front of the methodology section because certain variables have to be addressed rigorously in order to fully understand the models that are addressed in the methodology section.
3.1
Measurement of tail risk exposure
As mentioned in 2.2, a relative new, but appealing, way to measure bank-level risk, is by quan-tifying its exposure to the occurrence of extreme realizations of market variables. The market variable being the bank’s own stock return. It was argued that realizations of the stock’s return can provide valuable insight on the bank’s inherent risk.
Therefore, in line with the literature and with Ellul and Yerramilli (2013), the variable of interest is the daily log-return of the BHC’s stock. The BHCs are listed either on the NASDAQ or NYSE and their stock price data is obtained via the CRSP database. To measure tail risk exposure, I define it as a BHC’s one-day expected shortfall (ES) on it stock in a specific year at the 0.99 percentile. This percentile is chosen as it closely matches Basel III’s Value-at-Risk (VaR) and ES percentiles for market risk (Bank for International Settlement, 2016). Market risk most closely resembles the risk at hand. I choose ES over VaR as risk proxy because ES is a coherent risk metric as opposed to VaR. However, Subsection 3.2 defines other academically used risk metrics which do not run as deep in the tails and therefore form a robustness check for this proxy. To ultimately come up with ES, I first model the left tail of the return distribution of a BHC in a specific year. As mentioned earlier, the tails of a stock return’s distributions in general do not behave as a normal distribution suggests. This applies commensurately to BHCs. To properly model these tails, I apply Extreme Value Theory (EVT). The reason to use this theory rather than directly use the empirical distribution is because tail realizations are limited in number. Therefore, to enable tail smoothing and extrapolation beyond the empirical realizations and include this in ES, EVT is applied. Roughly two types of models exist within the field of EVT, block maxima models and threshold exceedance models (McNeil et al., 2015). Both models use empirical return data to model the tail. However, as noted by McNeil et al. (2015), the latter type of models are more efficient in data usage and I therefore use these in favor of the block maxima models. The threshold exceedance models rest on the observation that the empirical tail distribution of the BHC’s returns can be modeled approximately as a Generalized Pareto Distribution (GPD). An exposition of the underlying assumptions and mathematical derivation is found in appendix B.
To model the tail I define: xi the negative of the daily log-return on a BHC’s stock in a specific
in the threshold does not influence the estimated ES to any significant extent. Stability tests which I have performed on ES with a varying threshold, compliment their findings. The number
of the negative daily log-returns xi of a BHC in a specific year that exceed τ, which I denote as
Nt, are substituted in the objective function below with two unknown parameters. These are
β and ξ, respectively being the scale and shape parameter, which will describe the tail of the return distribution for each BHC in a specific year. To be perfectly clear here, the parameters are therefore time-variant with a yearly interval and every BHC in every specific year will thus have different values on these parameters. However, to prevent the objective function below to ’look messy’ I have omitted the time-indexes. The choice for time-varying parameters is two-folded. In the first place, I use yearly observations for all variables in this study, and for sake of consistency it is applied here as well. In the second place, to model the risk for a BHC in a specific year, it’s rational to only use the daily return data from that year, as I want to measure the risk exposure in that specific year. The below stated objective function is maximized over β and ξ by numerical means via MATLAB. The mathematical derivation of the below stated function is found in appendix B. I refer to appendix E for the code I have written in MATLAB to perform the optimization to come up with the two parameter values.
ln L(ξ, β; (xi− τ )1, . . , (xi− τ )Nτ) = −Nτln β − (1 + 1 ξ) Nτ X i=1 ln(1 + ξ(xi− τ ) β ) (6)
This results in two parameters, β and ξ which describe the tail of the return distribution for an individual BHC for a specific year. This means that every specific BHC in a specific year has its own two parameters values. For instance, if a BHC in a specific year has a rather ’fat’ tail, then ξ is likely to be higher for that BHC in that year. Yet, these parameters are not readily interpretable in the sense that one parameter value describes more tail risk exposure than another. However, the parameters can be used to measure the one-day 0.99 percentile VaR, which can be used to measure the one-day 0.99 percentile ES. As mentioned in 2.2, by using EVT these measures smooth and extrapolate the tails beyond the few empirical observations that are available and therefore provide better insight in the full tail. To measure VaR, I apply a 0.99 percentile and substitute
the threshold τ, the count of the negative log-returns that exceed the threshold Nt and the count
of the total return observations in a specific year for the BHC N, in the following equation:
V aR0.99 = q0.99(F ) = τ + β ξ(( 1 − 0.99 Nτ N )−ξ − 1) (7)
Note again that time-indexes to show that we are dealing with time-variant parameters, are omitted to prevent ’messy’ equations. This results in a BHC’s one-day VaR in a given year. It is a statistical risk measure which quantifies the negative one-day return which will not be exceeded upon with a statistical probability of 99 percent. Based on this VaR measure the one-day ES can be obtained, by taking the integral over the calculated VaR at the 0.99 percentile. This
equals substituting the VaR of the BHC in a given year denoted as VaR0.99, which has just been
calculated, and β , ξ , and τ, which are already known, in the following equation:
ES0.99 = 1 1 − 0.99 Z 1 0.99 q0.99(F )dx = V aR0.99+ β − ξτ 1 − ξ (8)
BHC in each specific year, ES0.99 is calculated and a proxy for tail risk exposure is obtained. A
BHC that has a higher one-day ES at the 0.99 percentile in a specific year than another BHC, has more tail risk exposure in that year, all else equal.
3.2
Alternative measures of risk
As elaborated on in the literature review, a wide-range of alternative risk proxies exist in academic literature to measure risk at a bank-level. The previous subsection’s model and risk proxy is a well-known and sophisticated way in risk management to model tail risk. However, as with many models, it makes assumptions on the behavior of stock returns which are not fully met in reality. In line with other studies and from a robustness point of view, I also use other proxies for risk exposure. This subsection will shortly elaborate on them.
The first alternative metric is based on Ellul and Yerramilli (2013). This risk metric is the
arithmetic average of the worst 2.5 percent returns on a BHC’s stock in a specific year. This provides an empirically based ES. The seven worst returns in a specific year for a BHC are summed up and the arithmetic average is taken. This provides the first alternative risk measure. Another often used proxy for risk exposure is the ratio of impaired loans to assets or to tier-1 capital (Ellul and Yeramilli, 2013) This metric is likely one of the drivers of the earlier given market-based risk proxies. These metrics are based on the market’s perception about the BHC’s value (assuming these perceptions are rational). A higher degree of impaired loans in relation to tier-1 capital makes banks more prone to solvency risk. This as a result will likely increase the tail risk exposure on the BHC’s stock returns.
The last metric that is often used in the academic literature (see: 2.2), is the volatility, or some-times the idiosyncratic component’s volatility, of the returns on the BHC’s stock (Laeven and Levine, 2009; Ferreira and Laux, 2007). To estimate the volatility of stock returns, I acknowledge the existence of volatility clustering, especially during the crisis (see appendix F), and account for that by estimating a GARCH(1,1) model (Bollerslev, 1986). I check for stationarity in the time-series, model the series as an AR(1) process, unless information criteria give me indication of using an alternative ARMA-process, and let the variance equation be based on GARCH(1,1). To come up with this metric, for every BHC I estimate the following conditional variance equation:
σ2t = α0+ αi∗ p X i=1 νt−j2 + βj ∗ q X j=1 σ2t−j (9)
Constraint on a0 > 0, ai> 0 and Bj> 0. νt−j2 is the jth-period squared lagged residual of
the mentioned AR(1)- or ARMA-processes used to model the time-series. σt−j2 is the jth-period
lagged GARCH term. Because I estimate a GARCH(1,1) model, the summation operators are
superfluous in this case. Taking the square root of the conditional variance, σ2t, provides the
3.3
Measurement of strong governance and risk oversight (GSI)
To ultimately come up with one variable which quantifies the strength of the governance and risk oversight (often abbreviated as governance strength) within a BHC in a specific year and as such is the independent variable of interest, I follow a few steps. In the literature review I have defined characteristics, which the academic literature deems to be contributers of a strong governance framework. These characteristics in turn will then, by statistical means which I will elaborate on shortly, be compressed to one single variable which proxies for the governance strength.
Based on the literature review in section 2.1, Table 1 provides the characteristics which define the strength of the governance framework in place in each individual BHC in a specific year. I have divided them in three separate categories; board structure, risk oversight embeddedness and compensation. The sub-categorization is for expositional purposes. However, these categories cover a substantial amount of the characteristics that can define the strength of the governance framework (see: 2.1). To my knowledge, no other empirical work has manually collected such an extensive coverage of governance characteristics and compressed it in one metric.
As noted by Faleye and Krishnan (2017), it is common in corporate governance literature to compress multiple governance characteristics in one comprehensive metric. Different methods to compress the characteristics in one metric have their relative merits and cons. For instance, I cannot merely sum the values of these characteristics and state that a BHC which has a higher value in a year had a stronger governance framework in place than a BHC with a lower value. Faleye and Krishnan (2017) use four characteristics and give each characteristic one point when it is available at the specific firm, thereby having an index ranging from one to four. However, this approach is too arbitrary. Therefore, to come up with one measure of governance strength, I have to follow a more formal and less arbitrary approach.
I follow Ellul and Yerramilli (2013) in the application of a principle component analysis on the governance characteristics. They use this to encompass different characteristics of a BHC’s risk management in one metric, a so-called Risk Management Index. Before I move on to explain this principle component analysis, I expect for the characteristics shown in Table 1, at the most basic level, that a BHC having a higher value on an individual characteristic indicates that this BHC has a stronger governance framework than a BHC with a lower value, all else equal.
factor loadings on my first principle component multiplied by the values on each characteristic, is the value that GSI takes for a BHC in a specific year. Intuitively, this first principle component captures most of the variation that exists between the characteristics. It therefore more or less, albeit depending on how much variation is captured, summarizes the different characteristics in one value without losing too much meaningful information (variation) in the data. A BHC with a higher first principle component, a higher GSI that is, than a BHC with a lower first principle component, a lower GSI that is, is expected to have a lower tail risk exposure, all else equal. Based on argumentations by Tetlock (2007) I perform the principle component analysis for each specific year, to avoid any look-ahead bias.
Table 1
The below stated table provides the governance structure and risk oversight characteristics which form the compo-nents of the (Alternative) GSI metric. I refer to appendix D for an elaboration on the characteristics. The variables are manually collected from the mentioned data sources through the SEC’s Edgar System.
Characteristic GSI Alternative GSI Metric Data source Board structure
Independent directors / Board size X X Ratio DEF 14A SEC CEO is not board chairman X X 1/0 DEF 14A SEC Number of board committees X Integer DEF 14A SEC Risk oversight embeddedness
CRO or equivalent is appointed X X 1/0 10-K SEC CRO or equivalent is an executive X X 1/0 10-K SEC Separate board risk committee X X 1/0 DEF 14A SEC Number of meetings risk committee X Integer DEF 14A SEC Experienced risk committee X X 1/0 DEF 14A SEC
Strong risk committee X X 1/0
-Compensation
CRO or equivalent top five paid X X 1/0 DEF 14A SEC
3.4
Alternative measures of strong governance
3.5
Control variables
To properly disentangle the effect that a strong governance has on tail risk exposure and overcome omitted variable bias, I control for the most important bank characteristics that are used in the academic literature. These are divided in five categories: general financial indicators, asset quality, time-variant risk preferences, capital adequacy and M-A-activity and are shown in Table 2. An extensive explanation of these variables is found in appendix D. There is no need to control for any country specific variables as for instance done by Laeven and Levine (2009). This is because the sample of this study only includes BHCs incorporated in the United States. As an extension of this, and as acknowledged by Adams and Mehran (2012), the BHCs are all regulated by the same regulator, the Federal Reserve, and the results therefore already control for regulation at the BHC level. Given that the, especially larger, BHCs often operate nationwide, controlling for state specific variables is not doable. In theory, this could be overcome by means of a proxy which is choosing the state where the operations are the largest, however this proxy is expected to be too noisy. Any other time-invariant heterogeneity is accounted for in the models as will be discussed in 4.1.
Table 2
The below stated table provides the variables which will be the control variables of this study. These are based on papers as discussed in Subsection 2.3. An elaboration on the exact definition of the variables is found in appendix D. The below discussed variables are obtained through the database of Bureau van Dijk: Orbis Bankfocus.
Characteristic Metric Explanation General financial indicators
Size ln of integer BHC’s asset value, scaled by the natural logarithm Return on assets (ROA) Ratio EBT divided by BHC’s asset value
Gross loans / Assets Ratio Outstanding loans divided by BHC’s asset value Loan concentration Scale 0-1 HH-index (HHI) of BHC’s loan concentration Asset quality
Impaired loans / Tier-1 capital Ratio Loans classified as impaired divided by Tier-1 capital Loan loss reserves / Impaired loans Ratio Reserves for loan losses divided by impaired loans Time-variant risk preferences
Fin. assets for hedging / Assets Ratio Fin. assets for hedging divided by BHC’s asset value Fin. assets for trading / Assets Ratio Fin. assets for trading divided by BHC’s asset value Capital adequacy
Tier-1 capital / Assets Ratio Capital designated as Tier-1 divided by BHC’s asset value Consumer deposits / Total funding Ratio Consumer deposits divided by available capital
Mergers and acquisitions
3.6
Descriptive statistics
I now move on to start the analysis of the data. Table 3 provides the descriptive statistics of all relevant variables of this research over the whole time-period. I will not discuss all the variables in great detail, but will highlight some of the most insightful observations.
Starting with the risk metrics, dependent variables that are; the mean tail risk exposure is 9 percent. This means that on average over the period 2006-2014 the BHCs had a tail risk exposure, daily ES that is, of 9 percent. Based on the alternative tail risk metric this is 6.8 percent. I will skip on the governance metrics, I will discuss these in Table 5. The average BHC had 174 billion of assets on its balance sheet, but high skewness exists in the distribution of assets, hence the size metric normalizes this by taking the natural logarithm of assets. The median tier-1 to asset ratio is 10.3 percent. However, some BHC experienced substantial downward pressure on their tier-1 capital during the financial crisis. For most BHCs, most of their assets exists out of loans averaging on 61 percent. These loans are mostly funded with consumer deposits, which on average makes up almost 80 percent of their total funding. Impaired loans, on average, make up about 13 percent of total tier-1 capital of BHCs. However, at the onset of the financial crisis, these values were a lot higher, sometimes even almost exceeding tier-1 capital, making recapitalization and use of the Troubled Asset Relief Plan (TARP) necessary.
In now move on to Table 4, which provides insight in how the components of the GSI metric move over time. Across the board, GSI has increased substantially, almost doubling in size with a noteworthy jump in 2010. Given that these metrics are lagged on year, this jump occurred in 2009; a year after the financial crisis hit ground. Over time, the number of board committees has increased from roughly four to five. Before the onset of the crisis, the Chief Risk Officer was already present at 76 percent of the BHCs, however at the end of the period this has increased to almost all BHCs having such a designated officer. The existence of a separate risk committee has increased dramatically after the financial crisis, in line followed with the number of meetings of such a committee and a member of that committee having industry experience.
Moving on to Table 5, which presents the correlation matrix for the aforementioned variables. I will just address a few observations. Lagged GSI seems to correlate negatively with tail risk exposure; which is expected. GSI seems to be highly correlating with size, suggesting that larger BHCs seem to have a higher governance strength. Larger BHCs seem to be more actively engaged in trading financial assets than their smaller counterparts. While insightful to some extent, pair-wise correlation lacks sophistication to make any inferences possible.
Table 3 and 4
Table 3 provides summary statistics on the risk metrics, governance structure and risk oversight characteristics, which form the GSI measure, and BHC characteristics. A definition of the variables is found in appendix D. Data on the risk metrics is over the period 2006-2014, data on the other variables are one-period lagged variables and thus cover the 2005-2013 period. 1 This is the non-lagged ratio of impaired loans to Tier-1 capital. 2 This is the one-period lagged ratio of impaired loans to tier-1 capital. Table 4 provides insight in the behavior of the governance structure and risk oversight embeddedness characteristics, which form the GSI measure, over time. The numbers link to the characteristics Table 3. For instance, [1] is the ratio of independent directors / Board size. This is done for the purpose of comprehensibility. Note that all metrics in table 4 are lagged one year, i.e. the value in 2006 is actually the observed value in 2005, because as mentioned, interest is in the impact that one period lagged GSI has on tail risk exposure.
Mean Median St. dev 25P 75P N Risk metrics
Tail risk exposure 0.090 0.062 0.076 0.041 0.105 468 Alternative tail risk exposure 0.068 0.050 0.049 0.033 0.083 468 (Impaired loans / Tier-1 capital)1 0.130 0.089 0.176 0.043 0.169 468
Volatility 0.049 0.033 0.050 0.023 0.057 468 Governance structure and risk
oversight characteristics
Independent directors / Board size [1] 0.812 0.833 0.100 0.750 0.900 468 CEO is not the board chairman [2] 0.331 0.000 0.471 1.000 0.000 468 Number of board committees [3] 4.606 5.000 1.233 4.000 5.000 468 CRO or equivalent in appointed [4] 0.873 1.000 0.333 1.000 1.000 468 CRO or equivalent is an executive [5] 0.831 1.000 0.378 1.000 1.000 468 Separate board risk committee [6] 0.597 1.000 0.491 0.000 1.000 468 Number of meetings risk committee [7] 3.852 4.000 3.857 0.000 6.000 468 Risk committee experience [8] 0.449 0.000 0.498 0.000 1.000 468 Strong risk committee [9] 0.203 0.000 0.403 0.000 0.000 468 CRO or equivalent top five paid [10] 0.367 0.000 0.482 0.000 1.000 468 GSI 3.889 3.999 2.417 1.499 5.782 468 Alternative GSI 1.473 1.432 0.686 1.020 2.123 468 BHC characteristics Assets (bln) 174.8 16.17 468.4 86.09 704.9 468 Size 24.04 23.51 1.700 22.88 24.98 468 ROA 0.008 0.010 0.012 0.006 0.013 468 Tier-1 capital / Assets 0.107 0.103 0.032 0.088 0.120 468 Gross loans / Assets 0.610 0.661 0.166 0.554 0.719 468 Loan concentration 0.390 0.348 0.173 0.298 0.403 468 Consumer deposits / Total funding 0.797 0.814 0.115 0.740 0.886 468 (Impaired loans / Tier-1 capital)2 0.127 0.086 0.177 0.036 0.169 468
T able 4 and Figures 1, 2 and 3 T able 4 b elo w pro vides the pair-wise correlation b et w een some of the k ey v ariables that are used in this study . Figures 1, 2 and 3 sho w ho w the tail risk exp osure metric mo v es with the alternativ e tail risk exp osure measure, the ratio of impaired loans to tier-1 capital and GA R CH(1,1) estimated v olatilit y . T ai l ri sk exp osure GSI Size R O A Tier-1 capital / Asssets Gross loans / Assets Loan concen- tration Con- sumer dep osits / Assets Impaired loans / Tier-1 capital Loan loss reserv es / Imp. loans
Finan. Assets for hedging /Assets Finan. Assets for
4
Methodology
4.1
Panel-data framework
To measure the impact that a strong governance and risk oversight framework in a BHC, as measured by GSI (see: 3.3), has on its tail risk exposure (see: 3.1), I use a panel-data framework over the period 2006-2014. In this framework, GSI and the control variables are lagged one-period. This convention is in line with Ellul and Yeramilli (2013).
The sample consists of 53 U.S. BHCs which have been randomly selected out of the population of U.S. BHCs existing and listed in 2008 to avoid survivorship bias. The BHCs with their governance strength value (GSI) before the onset of the financial crisis (2007) can be found in appendix A. Specifically, I use the following model as building block for the different specifications under which I test the main hypothesis:
T ail riski,t = α + β ∗ GSIi,t−1+ γ ∗ Xi,t−1+ κi+ ηt+ νi,t (1)
Here Tail riski,t is a vector of a BHC’s one-day ES in a specific year as defined under 3.1, GSIi,t−1
is a vector of one-period lagged values on GSI as defined under 3.3 and Xi,t−1 is a vector of
one-period lagged BHC characteristics as defined under 3.5. κ are BHC fixed effects to account for time-invariant heterogeneity which are applied is some specifications, η are time-period fixed effects to account for BHC-invariant heterogeneity which are applied in all specifications and ν is an idiosyncratic disturbance term. Under all specifications standard errors are robust towards heteroskedasticity and under some specifications are clustered at the BHC-level. As argued, from
a robustness point of view, Tail riski,t and GSIi,t−1 will exhibit different proxies as defined under
3.2 and 3.4. However, the general framework remains the same.
To measure the second hypothesis, which is on whether I can find support for a hedging channel of risk taking (see: 2.4) and to get a feeling on whether potential endogeneity might be prevalent, the following simple cross-sectional model is used:
∆ GSIi,2009−2011 = α + β ∗ Exposurei+ γ ∗ Xi,2008+ νi (3)
As argued in Subsection 2.4, note that model is not rigorous in addressing endogeneity and only can give an indication of whether it might be prevalent. This is because if BHCs who experienced more risk increase their governance strength more prominently than those who did experience less risk, then risk is likely driving a significant part of governance strength (Fahlenbrach, Prilmeier and Stulz, 2012). However, the model discussed in subsection 4.2 treats potential endogeneity
more rigorously. In the model shown above, ∆ GSIi,2009−2011 is a BHC’s change in GSI over the
period 2009-2011. Exposurei is a dummy variable which takes on one if the BHC had a larger
than the median tail risk exposure during the crisis (2008-2009) and zero otherwise. Xi,2008 are
BHC characteristics in the year 2008. Standard errors are robust towards heteroskedasticity. To address the last hypothesis of an overall increase in governance strength within BHCs due to enhanced legislation and supervisory scrutiny, the following model, that is based on Ellul and Yeramilli (2013), is used:
Post2009t is a dummy which takes on one after 2009 and zero before. κ are BHC fixed effects to
account for time-invariant heterogeneity which are applied is some specifications, η are time-period fixed effects to account for BHC-invariant heterogeneity which are applied in all specifications and ν is an idiosyncratic disturbance term. Under all specifications standard errors are robust towards heteroskedasticity. Note that, as argued in 2.4, that for a proper economic interpretation on the reason why the dummy has a given coefficient it is necessary to rule out a potential endogenous interaction of the governance strength and tail risk when I address the main hypothesis.
4.2
Addressing endogeneity: dynamic panel GMM-estimator
As argued by Wintoki et al. (2012), (dynamic) endogeneity, can plague and bias results found in a corporate governance setting. As noted by for instance Adams and Mehran (2012), there is a high complexity in dealing with this endogeneity in a corporate governance setting. Ideally, an IV Two-Stage Least Squares is used. However, it is extremely difficult to find a strong instrument which in the context of time invariant heterogeneity has enough time variation. Many studies use ad hoc measures to circumvent this problem to some degree, for instance by using weak instruments (Staiger and Stock, 1997). But Adams and Mehran (2012) and Ferreira and Laux (2007) note that the chosen instruments often still lack their desired properties.
In line with Ellul and Yeramilli (2013) and Andres and Vallelado (2008), I choose to address the endogeneity problem and test my main hypothesis by using a GMM-estimatior in a dynamic panel. The model developed by Holtz-Eakin, Newey and Rosen (1988) and Arellano and Bond (1991), while later augmented by Arellano and Bover (1995), lends itself in this context while addressing conventional problems with dynamic panels. While appealing, Roodman (2009) notes that the model’s high complexity might work like a ‘black box’ for those who are not familiar with these type of models. For instance, in the original Arellano and Bond (1991) model, the two-step GMM iteration process, which is assumed to perform better (Windmeijer, 2005), would provide downward biased standard errors to the point that any inferences made are useless. Windmeijer (2005) introduced finite-sample corrected standard errors which can accommodate for this problem while still being able to use the two-step iteration process. In this context, it is unclear whether the study by Ellul and Yeramilli (2013) did use these corrected standard errors and therefore how strong their inferences are based on this model.
GMM has the desirable asymptotic properties such as efficiency and consistency, provided that the overidentifying moment conditions are not violated. However, it may perform poorly in finite samples. In the context of the dynamic panel, where interest is still in the impact that the governance strength has on tail risk, but now accounting for dynamic endogeneity, the model
introduces several elements to account for this possible endogeneity. These elements are the
exogenous. The following model forms the untransformed basis for the GMM-estimatior:
T ail riski,t = α + ω ∗ T ail riski,t−1+ β ∗ Alternative GSIi,t−1+ γ ∗ Xi,t−1+ κi+ ηt+ νi,t (4)
The Hansen-test for overidentification measures whether the assumption that the system is overi-dentified can be rejected. Hence, if this assumption cannot be rejected, the applied instruments are assumed valid. This does not say anything about the validity of the model itself. Another im-portant consideration is serial correlation at the second order. Since the errors are assumed white noise, their first differences are expected to be a MA(1)-process. Therefore, there is no interest in the first order lags. However, serial correlation at the second order should be non-existent to let the moment conditions be valid. Roodman (2009) developed the command “xtabond2” in STATA to perform the necessary estimation while being able to apply the Windmijer (2005) finite-sample correcting standard errors which is to overcome bias in the asymptotic standard errors.
I acknowledge that the choice to treat the other control variables (see 3.5), apart from time-variant preferences, to be exogenous is open to debate. Therefore, in the context of the risk proxy GARCH(1,1) estimated volatility, (see 3.2) I use the same model, but now treat one-period lagged ROA and the ratio of consumer deposits to total funding as potentially endogenous in the system as well. There are good arguments in favor of this choice (Arellano and Bover, 1995), since both are likely not strictly exogenous in relation to volatility. The untransformed basis therefore is as follows:
V olatilityi,t = α + ω ∗ T ail riski,t−1+ β ∗ Alternative GSIi,t−1+ γ ∗ Xi,t−1+ κi+ ηt+ νi,t (5)
4.3
Robustness checks
The alternative proxies for both (tail) risk exposure and governance strength by themselves provide a robustness check. Moreover, the GMM-estimator is a robustness check on whether the panel data results are not suffering from potential dynamic endogeneity. However, I will perform some additional robustness checks.
Specifically, I estimate the panel-data framework as described under model 1, but bootstrap the standard errors based on 1000 replications. Additionally, I run a GLS-RE panel framework; a Gen-eralized Least Squares estimation method using time-period dummies, but using random effects for the BHCs under the assumption that the variation across the BHCs is random and uncorre-lated with the model’s regressors (Wooldridge, 2002). In that case, RE is more efficient than BHC fixed effects. Further robustness checks are in the spirit of Ellul and Yeramilli (2013). I use a first-differenced (FD) model instead of fixed effects to deal with time-invariant heterogeneity; while both yield the same result when there are only two time-periods this is not the case when there are more time-periods. Additionally, I modify the way I measure governance strength denoted as GSI-FW (see: 3.4).
5
Empirical results and analysis
This section provides the empirical results and analysis by using the models from the previous section to answer the stated hypotheses. This section starts with a treatment of the second and third hypothesis. Based on these insights, the thereafter following subsections will thoroughly address the main hypothesis.
5.1
Panel framework - structural differences in BHCs’ GSI
Before addressing the main hypothesis, I start the analysis in the context of the second and third hypotheses (see: 2.4). This Subsection 5.1 is therefore aimed at getting a feeling of, and finding whether there are, differences in BHCs’ characteristics and their governance strength. Moreover, addressing the second hypothesis provides us with a first grasp on whether endogeneity might be prevalent. However, as must be noted, the model used in this section to address this hypothesis is a ’simple’ cross-sectional model. In a later subsection (see: 5.5), a rigorous and sophisticated model is used to address and account for potential endogeneity properly to make meaningful inferences. To start with the second hypothesis, which is aimed at finding whether BHCs which had a larger than median tail risk exposure during the financial crisis increased their governance strength more than those who did not had such a substantial risk exposure. As argued in Subsection 4.1 the following cross-sectional model is estimated:
∆ GSIi,2009−2011 = α + β ∗ Exposurei+ γ ∗ Xi,2008+ νi (17)
If those BHCs which had the largest risk exposure during the financial crisis, as measured by
Exposurei, have increased their governance strength the most, then this supports the hedging
Table 6
The below stated table provides the estimation output of a panel-data regression on the relationship between lagged GSI and tail risk exposure over the period 2006 – 2014 for 53 Bank Holding Companies. The definition of the variables can be found in appendix D. κ and η are BHC- and time period fixed effects to accommodate for time- and BHC-invariant heterogeneity, respectively, that are used in different specifications as shown in column [1] through [4].
∆ GSIi,2009−2011= α + β ∗ Exposurei+ γ ∗ Xi,2008+ νi GSIi,t= α + β ∗ P ost 2009t+ γ ∗ Xi,t−1+ κi+ ηt+ νi,t
Standard errors are robust towards heteroskedasticity unless stated otherwise. I use ***, ** and * to denote statistical significance at the 0.01, 0.05 and 0.10 level, respectively.
Δ2009−2011 GSIt GSI [1] [2] [3] [4] Post 2009t 1.419*** 1.539** 1.837*** (0.464) (0.466) (0.604) Exposurei -0.402 (0.508) Sizet−1 0.294 0.559*** 0.538*** -0.537 (0.192) (0.083) (0.084) (0.649) ROAt−1 -21.635 -19.350* -21.177** -19.589* (28.881) (10.026) (10.656) (11.131) (Tier-1 capital / Assets)t−1 13.097* -2.253 -2.045 2.712
(7.085) (2.934) (3.000) (5.189) (Gross loans / Assets)t−1 -0.176 -0.298 -0.836 1.937
(1.122) (0.875) (0.989) (2.473) Loan concentrationt−1 0.414 -0.193 -0.004 -2.259***
(1.491) (0.705) (0.743) (0.679) (Impaired loans / Tier-1 capital)t−1 1.591* 0.767 0.640 0.176
(0.876) (1.190) (1.181) (0.451) (Loan loss reserves / Impaired loans)t−1 0.106 0.0247 0.047 0.168*
(0.876) (0.095) (0.091) (0.094) (Consumer deposits / Total funding)t−1 -0.801 0.321 0.134 0.478
(3.416) (1.132) (1.265) (2.244) (Finan. assets for hedging / Assets)t−1 -4.855 -4.142*** 2.795
(4.036) (1.346) (3.232) (Finan. assets for trading / Assets)t−1 -2.926 -2.807 -5.851
(9.192) (3.888) (11.130) M-At−1 -0.251 -0.215 -0.125 -0.182 (0.851) (0.233) (0.232) (0.210) Constant 6.728 -9.831*** -8.856*** 14.931 (6.036) (3.068) (3.132) (16.310) Observations 53 415 415 415 R2 0.377 0.273 0.285 0.306
Time-period FE - Yes Yes Yes
BHC FE - No No Yes
Moreover, the notion that there is no support for the hedging channel provides some indication that endogeneity might not be prevalent. However, I must be very cautious with such an interpretation because the model is not specified to make these kind of inferences. Therefore, I defer making any inferences on endogeneity to Subsection 5.5.
The third hypothesis is addressed now on whether, across the board, BHCs increased their gover-nance strength after the financial crisis. The question might be a stating of the obvious because of enhanced legislation and greater supervisory scrutiny after the financial crisis. However, as argued, the economic driver of this increase is harder to establish. The enhanced legislation might be driving the increase, but the risk exposure might be driving the results as well. However, as was found under the second hypothesis, there is no support for a hedging channel of risk taking. I defer any hard inferences on the economic interpetation to Subsection 5.5 after I have established more confidence on the endogeneity issue. For now the following model, as argued in 4.1, is estimated:
GSIi,t = α + β ∗ P ost 2009t+ γ ∗ Xi,t−1+ κi+ ηt+ νi,t (16)
Here GSIi,t is a vector of values on GSI as defined under 3.3, Xi,t−1 is a vector of lagged BHC
characteristics as defined under 3.5, Post2009tis a dummy which is one after 2009 and zero before.
ηt are time-period fixed effects used under all specifications to account for BHC-invariant
hetero-geneity. κi are BHC fixed effects to deal with possible unobserved time-invariant heterogeneity;
these are used in some specifications. Standard errors are robust towards heteroskedasticity. The estimated output is shown in Table 6. Column 2 shows that, as expected, the coefficient on
the POST2009tdummy is statistically and economically significant and positive in sign. Moreover,
larger BHCs have a stronger governance framework. This is also supported by Ellul and Yeramilli (2013), but then in the context of the risk management function. In column 3, two proxies for time-variant risk preferences are introduced (see: 3.5). The introduction of these proxies shows that one proxy, the ratio of financial assets for hedging purposes to assets, is significant and negative in sign. This means that BHCs which hedge more of their risk by means of derivatives, have a governance framework which is less strong. Part of the story can be explained, at least for the governance characteristics on which the BHC’s board or management has control. For the characteristics on which they have no control, for instance because these are set by legislation, the following argument can not be used. However, one might argue that BHCs appoint a CRO, but do not make the CRO an executive because they feel that much of the risk is already hedged by means of derivatives, thereby making the need for an executive CRO less necessary. In this way, GSI is lower (recall that I mentioned that all characteristics positively contribute to the GSI value). In column 4 I introduce BHC fixed effects; this changes the interpretation of the coefficients to a
within BHC effect as noted by Adams and Merhan (2012). However as expected, the POST2009t
dummy remains significant and positive in sign.
5.2
Panel framework - relationship GSI and tail risk exposure
As stated in Subsections 2.4 and 4.1, the main hypothesis’ interest is on the impact that one-period lagged GSI has on tail risk exposure. To properly estimate this relationship, as a first start, the following model, as discussed in 4.1, is estimated:
T ail riski,t = α + β ∗ GSIi,t−1+ γ ∗ Xi,t−1+ κi+ ηt+ νi,t (10)
Here Tail riski,t is a vector of tail risk exposure as defined under 3.1, GSIi,t−1 is a vector of
one-period lagged values on GSI as defined under 3.3, Xi,t−1 is a vector of one-period lagged
BHC characteristics as defined under 3.5. κ are BHC fixed effects to account for time-invariant heterogeneity which are applied in some specifications, η are time-period fixed effects to account for BHC-invariant heterogeneity which are applied in all specifications and ν is an idiosyncratic disturbance term. Under all specifications standard errors are robust towards heteroskedasticity and under some specifications are clustered at the BHC level. The output is shown in Table 7. Column 1 provides the output while controlling for different BHC characteristics, (see: 3.5), and BHC-invariant heterogeneity. In this specification, lagged GSI is statistically significant and negative in sign; as expected. Size does not seem to be statistically important in explaining tail risk, which is in line with Elull and Yeramilli (2013), but is different from the findings of John, Litov and Yeung (2008). However, it must be noted that the latter study focuses on manufacturing firms, rather than banks. Return on assets (ROA) is significant and negative in sign which is in line with most literature; better BHC financial performance, as expressed by its ROA, often leads to lower tail risk. Somewhat surprisingly, the BHC’s solvability, as expressed by its tier-1 capital to assets, does not seem to significantly impact tail risk, contradictory to the findings by Elull and Yeramilli (2013). The ratio of impaired loans to tier-1 capital seems to be a significant driver of tail risk; impaired loans are likely to be written off and as such, a substantial amount of impaired loans in comparison to tier-1 capital might give risk to another source of solvency risk. Therefore, the BHC is likely to have a larger tail risk exposure on its own stock return.
Column 2 provides the same output as in column 1 but, in the spirit of Elull and Yeramilli (2013), I now introduce two new control variables; the ratio of financial assets held for hedging purposes to assets and the ratio of financial assets held for trading purposes to assets. These variables might control for time-variant risk appetite of the BHCs. A higher degree of instruments held for hedging might indicate a more conservative appetite towards risk while a higher degree of instruments held for trading might indicate a more aggressive appetite towards risk. Therefore, the expected signs are negative and positive, for hedging and trading, respectively. After I introduce the two variables, GSI remains statistically significant and negative in sign. The larger use of financial assets for hedging purposes in comparison to assets on the balance sheet seems to substantially mitigate the tail risk exposure of the BHC, as financial theory suggest. It is noteworthy that Ellul and Yermamili (2013) actually found the exact opposite result, but note that the economical significance in their case is negligible.
