Capital regulation and financial stability of banks : are regulators shaping the right framework to prevent a new banking crisis?

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Capital Regulation and Financial Stability of Banks

Are regulators shaping the right framework to prevent a new banking crisis?

University of Amsterdam

Amsterdam Business School

MSc Finance

Master Specialisation Corporate Finance

Author:

B.J. Poos

Student number:

10199853

Thesis supervisor: dr. J.J.G. Lemmen

Finish date:

June 2016

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PREFACE AND ACKNOWLEDGEMENTS

I would like to thank my supervisor dr. J.J.G. Lemmen of the Faculty of Economics and Business at the University of Amsterdam and my supervisor Mr. N. Piepenbrink at KPMG Corporate Finance. Dr. Lemmen helped me when I had questions about my research and frequently provided me with useful feedback. He brought this dissertation to a higher academic level. I would like to thank Mr. Piepenbrink for the interesting input and the conversation we had about the research. Furthermore, I want to thank the employees and other interns at KPMG for helping me and making my graduate internship enjoyable.

I also want to thank my father and sister for their support during my study. Last but not least, I thank my friends, for being there for me and making my period as a student at the University of Amsterdam unforgettable.

NON-PLAGIARISM STATEMENT

By submitting this thesis the author declares to have written this thesis completely by himself/herself, and not to have used sources or resources other than the ones mentioned. All sources used, quotes and citations that were literally taken from publications, or that were in close accordance with the meaning of those publications, are indicated as such.

COPYRIGHT STATEMENT

The author has copyright of this thesis, but also acknowledges the intellectual copyright of contributions made by the thesis supervisor, which may include important research ideas and data. Author and thesis supervisor will have made clear agreements about issues such as confidentiality.

Electronic versions of the thesis are in principle available for inclusion in any UvA thesis database and repository, such as the Master Thesis Repository of the University of Amsterdam

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ABSTRACT

This research studies the impact of bank capital ratios on the financial stability of banks. The bank capital ratios that have been used in this study are Tier 1 capital ratio, Regulatory capital ratio and Capital Asset Ratio. The financial stability measures are defined as the ES, the VaR or the SDROA. The dataset consists of 138 listed banks in the U.S. over the period Q3.2007 till Q4.2016. The crisis period is defined as Q3.2007 till Q4.2009. The outcomes are as follows; 1) Banks with higher Tier1 and Regulatory capital are more stable during the crisis for the full sample of banks. 2) The Capital Asset Ratio shows no significant effects on the stability of the full sample of banks. 3) Complex risk-weighted capital ratios are better in explaining the stability of banks in comparison to a simple capital ratio. 4) Provision for Loan Losses is an important determinant to ensure stability through the full time period for banks. 5) When this study rerun the regressions for small, medium and large banks, Tier 1 and Regulatory capital have only a positive effect on the stability during the crisis for large banks and to a less extent for medium banks. 6) The Capital Asset Ratio helps to ensure stability for small banks during the crisis.

JEL Classification: C53, G01, G17 and G28. Keywords:

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LIST OF TABLES

Table 1 Summary statistics [16]

Table 2 Key variable expectations [23]

Table 3 Regressions of Tier 1 ratio on ES [26]

Table 4 Regressions of Regulatory ratio on ES [27]

Table 5 Regression of CAR ratio on ES [28]

Table 6 Regressions of capital ratios on VaR and SDROA [30] Table 7 Regressions small, medium and large banks on ES [32] Table 8 Regressions small, medium and large banks on VaR [33] Table 9 Regressions small, medium and large banks on SDROA [34] Table 10 Regressions of capital ratios on ES without TBTF banks [35]

Table 11 Regressions of Tier 1 after Black Monday [36]

Table 12 Regressions of capital ratios after crisis period [37] Table 13 Regressions of capital on ES with clustered standard errors [38] Table 14 Correlation table of the variables used in the base regression [47]

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LIST OF FIGURES

Figure 1 ES and VaR normal distribution [12]

Figure 2 Daily returns Bank of America [17]

Figure 3 Average of ES and VaR during the full period [17] Figure 4 Average of the bank’s capital ratios over time [18] Figure 5 Scatterplots of the stability over time for the Tier 1 capital [19]

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CHAPTER 1 Introduction

The global financial crisis, which began in the middle of 2007, has shown the weakness of banking regulations to systematic risk. The capital requirements of the Basel Accords, protecting banks against unexpected losses, have been insufficient to bear the excessive risk taking by banks and, consequently, to contain the number of bank defaults during the financial crisis. Therefore, the regulatory framework has been under scrutiny of regulators and academics to redefine the capital requirements with the aim of introducing new requirements which enhance the resilience of individual banks to financial shocks (Vallascas and Keasey, 2012).

The rules have been refined and broadened to cover various types of risk, differentiate among asset classes with different risk characteristics, and allow for a menu of approaches to determine the risk weights to be applied to each asset category. However, the increasing capital requirements do not imply that insolvency is remote, and that banks are not incentivized to take on more risk. Following Demirguc-Kunt, Detragiache and Merrouche (2013), the relationship between bank capital and risk is U-shaped. This implies that severely undercapitalized banks take the most risk, so they can profit from the deposit insurance. In the U.S. the Federal Deposit Insurance Corporation (FDIC) has introduced this measure to protect bank depositors, in full or in part, from losses caused by a bank’s inability to pay its debt when due. Whereas capital increases, the bank will take on less risk, until the capital again reaches high levels, banks will increase their risk exposure. The high capitalized banks take more risk to benefit from the upside, because they are better resistant to financial shocks. The Basel Accord uses different capital ratios from complex risk-weighted capital ratios to simple leverage ratios. Further, in the process of the new Basel Accords, the rules of the risk-weighted capital ratios have become increasingly elaborate, reflecting the growing complexity of modern banking. This results in a competitive advantage for large financial institutions, which have a large asset base, that can artificially increase their risk-weighted capital ratios (Estrella, Park and Persistiani, 2000). Also, Berger and Bouwman (2013) stress that the financial crisis has caused doubt regarding the use of minimum capital requirements to prevent bank instability. Given that, the capital requirements were not able to prevent banks from insolvency and bankruptcy. Management of banks claim that more capital leads to higher financing costs, whereas economists argue that this increase in cost will be limited (Bijlsma and Zwart, 2010). Also, management of banks complains about the implementation costs related to the Basel Accords III, which may also affect the stability of banks.

Due the contradictory literature about bank capital and its effect on financial stability this study seeks to investigate the impact of capital ratios on bank stability and seeks to investigate whether higher capitalized banks can be considered more stable against a financial shock like the recent financial crisis.

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8 This results in the following research question of this thesis:

Are higher capitalized banks more stable against financial shocks? More in detail: Have banks with higher Tier 1 capital ratio, Regulatory capital ratio or Capital Asset Ratio a higher ES during the crisis period of Q3.3007 till Q4.2009 and the full period Q3.2007 till Q4.2016?

The results of this study might be useful for regulators in shaping capital requirements in the Basel III framework and as a validation of the current requirements. To provide further answers, this research also questions which types of capital ratio: core Tier 1, Regulatory capital, which consists of core Tier 11_{and Tier 2, or Capital Asset Ratio (CAR), are most related to financial stability of banks. This is} important for regulators to consider if the ratios reflect the actual risk exposure. For example, it may be the case that simpler ratios are better in explaining the risk exposure as opposed to Regulatory capital. Therefore, this study tests the following capital ratios: Tier 1 over risk-weighted assets and Regulatory capital, which consists of core Tier 1 and Tier 2, over risk-weighted assets. And the simpler ratio that will be tested is the Capital Asset Ratio2_{. The Basel Committee has increased these minimum capital} requirements and rules throughout the past years as displayed in APPENDIX A. The capital ratios will be tested on the following stability measures: Expected Shortfall, Value at Risk, and the standard deviation of the return on assets.

This study adds value to the existing literature in several ways. Demirguc-Kunt, Detragiache and Merrouche (2013) examine the impact of financial shocks by using stock returns as dependent variable. However, stock return is a proper measure for profitability and Expected Shortfall (ES), Value at Risk (VaR) and standard deviation of return on assets (SDROA) are better measures for stability. Given that, these ratios are better in predicting the potential maximum loss of a stock (Tsay, 2010). Second, VaR and ES are official quantitative risk metric systems of the Basel Committee on Banking Supervision (Chang, 2015). The financial crisis period is defined as Q3.2007 till Q1.2009 and a period after the crisis from Q2.2009 till Q4.2016, which is an extended period in comparison to Demirguc-Kunt, Detragiache and Merrouche (2013). Further, this article uses in comparison to the literature three different measures for capital ratios and for financial stability. Finally, this study differentiates itself by dividing the sample of banks in three different subsamples based on size in assets. This will be done solely on assets in three quantiles of the dataset. So, this study contributes to this discussion if size matters for capital regulation and vice versa, which capital ratio is most effective in explaining financial stability and whether differences exist between applicable ratios for different sized banks.

The outcomes of this study show that Tier 1 capital ratio, Regulatory capital ratio and the CAR have no positive effect on the stability of banks through the full period of time. However, Tier 1 and Regulatory capital have a positive impact on the ES during the crisis, which does not apply for the

1_{Core Tier 1 and Tier 1 are used interchangeably in this manuscript. However, we mean core Tier 1.} 2_{CAR =}𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦

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9 Capital Asset Ratio. So, banks with higher Tier 1 and Regulatory capital are better able to resist a financial crisis, which is in line with the study of Beltratti and Stulz (2012). Only, the Provision for Loan Losses has a significant impact on the ES through the period of time. This challenges the Basel Committee to find a way to reduce this amount on the balance sheet of banks to ensure more stability. The CAR, which is defined as a simple capital ratio, is not better in explain the stability of banks in comparison to the complex risk-weighted capital ratios in the full sample. This outcome is in contrast with the study of Demirguc-Kunt, Detragiache and Merrouche (2013). Besides this outcomes, this research uses an interaction term of assets and capital during the crisis. This term shows that banks of large scale have a negative impact on the stability during the crisis for Tier 1 and Regulatory. Nonetheless, this outcome is not robust when this study rerun these regressions without TBTF banks. TBTF banks may overly influence the results, since these kind of banks can take more risk, because they will be supported with financial help if they experience liquidity problems. The outcomes of this robustness test are in line with the research of Berger and Bouwman (2013). The regressions have been performed again on small, medium and large banks during the sample. The results are not in one line with the regressions on the full sample of banks. Tier 1 and Regulatory capital helps primarily large banks during the crisis on stability and to a less extent medium banks. The CAR seems effective in explaining the stability of small banks during the crisis. Furthermore, the Tier 1 capital has a positive effect on the ES during a potential new crisis as the robustness test of this research suggests. This paper shows that the Basel Committee has still not fulfilled his goal to shape a framework to ensure financial stability and limit systemic risk. The outcomes of this research implicates that it is important to make a framework of rules for different size of banks.

This research is build up as follows. In chapter 2 relevant theory and related literature are discussed on bank capital regulations. Next, chapter 3, describes the data collection and also the data characteristics. Thereafter in chapter 4, we show the methodology on the empirical model. In addition, the variables used in this research are explained in detail. Chapter 5 starts with the results of the empirical model and relates them to hypotheses. To verify the results, there are multiple robustness checks performed in chapter 6. Overall, these outcomes are discussed in chapter 7. Lastly, chapter 8 gives a conclusion about this study.

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CHAPTER 2 Literature overview

1.1 Theory

The banking system in the U.S. is the most heavily regulated sector of the economy. The first reason that the U.S. government provides regulation to the banking sector is to increase information available to investors. The second reason is to ensure the soundness of the financial system. Due the regulations the government tries to reduce the moral hazard and adverse selection problems that investors face in the banking sector (Akerlof, 1970)3_{. However, depositors also have to deal with these problems of} information asymmetry, therefore it is for their importance that they monitor the banks. Nonetheless, it is too costly for them to monitor as an individual a bank, hence they have, in general, a minor share in the bank. In addition, it is useless if active monitoring is performed by numerous depositors, because this leads to a free-riding problem. This problem is solved by introducing regulations that monitor and control the bank (Matthews and Giuliodori, 2012). The fact that regulations are necessary to alleviate the risk of systemic failure, emphasizes that banks may experience bank runs as they operate with a relatively illiquid asset base combined with a large amount of demand deposits. A bank run can happen as a consequence of asymmetric information that may lead to a global collapse of the financial banking system which is referred to as a financial panic. Depositors do not possess all the information to determine whether their funds at financial intermediaries can be considered as safe, therefore they may withdraw their funds out of the financial intermediaries. As a consequence, a bank has to liquidate a large part of its assets to cover its liabilities which will result in serious losses. Furthermore, this financial panic may serve as a springboard to a systemic crisis, due the contagious nature of bank runs (Santos, 2001)4_{. The deposit insurance introduced by the government has proven to be very successful in} protecting the banking system from bank runs5_{. Given that, depositors do not face the risk of losing all} their funds. Based on this diminished risk exposure, they have less incentive to actively monitor the bank and to ask a premium interest for the risk of their funds at the bank (Matthews and Giuliodori, 2012).

However, the deposit insurance also comes at the cost of moral hazard. Given that, the insurance company charges a flat premium for banks, they may engage in excessive risk taking by increasing the riskiness of their assets. This effect is stronger through the fact that depositors are not asking a premium that is in line with the risk of the bank, because they profit of the deposit insurance. This moral hazard problem can be approached from an option perspective. From this perspective, firms maximize their equity value by increasing the riskiness of the debt and/or equity level. In other words, it is the optimization of the value of a put option on the bank’s assets with a strike price equal to the face value of debt. Santos (2001) introduced a risk sensitive insurance premium to address the problem and to

3_{Moral hazard is the problem created by information asymmetry after a transaction when one person takes more}

risk, because someone else bears the cost of those risks. Adverse selection occurs before the transaction.

4_{Santos (2001) explains the theory of the contagious nature of bank runs.} 5_{Santos (2001) explains how theories try to save banks from runs.}

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11 regulate the bank’s capital structure. However, Chan, Greenbaum and Thakor (1992) proved that charging a risk sensitive insurance premium is not a solution to address this problem, because it is impossible to determine a fair premium for each bank. The minimum capital requirements introduced by the Basel Accords on bank capital seem to be the solution to mitigate the problem of moral hazard. Given that, regulators forcing banks to have some “skin in the game”, minimum capital requirements should curb incentives for excessive risk taking created by limited liability and amplified by bailout expectations and deposit insurance (Demirguc-Kunt, Detragiache and Merrouche, 2013). In addition, the capital works as a buffer for banks to resist financial shocks instead of a public bailout or becoming insolvent.

Researchers are still debating on the effect of capital regulation on the incentive of risk taking. Academics take two opposing views regarding the regulation on bank capital. For instance, in the articles of Furlong and Keeley (1989, 1990) the researchers claim that capital regulations limit risk taking. The results of these articles show that introducing a minimum requirement on capital, which results in an increase in capital, result in a lower risk-taking behaviour of a bank. They argue that listed banks seeking to shareholder maximization are not willing to increase the riskiness of their assets due an increase of capital standards. Following Merton (1977) the deposit insurance provides a bank the incentives to increase the riskiness of their assets. An increase in the amount of equity will lower relatively the leverage level. This will decrease the marginal value of the deposit insurance option, given a flat insurance premium, with respect to higher asset risk. Lastly, Santos (1999) also argues that due the stricter capital regulation banks have less incentive to take risk. Given that, stricter capital requirements result in higher bankruptcy costs due the lower level of leverage. In addition, it also results in increased funding costs as equity is more expensive than deposits or leverage.

In contrast, Koehn and Santomero (1980) show a positive relationship between capital regulation and risk taking by banks. The authors present a model within which the bank is not only the manager but also the agent. Therefore, the model implies that the bankers are risk-averse. In this research, the bankers set their asset portfolio such that it offers the highest expected return for the lowest level of risk on the efficient frontier. Nevertheless, the requirement of a minimum of capital regulation may increase the risk of the asset portfolio. Given that, Koehn and Santomero (1980) argue that banks may take more risk to compensate for the losses in expected return, because of the lower level of leverage and the relatively higher costs of equity in comparison with debt. As a result, this may lead to a higher chance of default of the banks. It can be concluded that there is still no consensus if higher capital requirements may lead to a higher probability of default. Rochet (1992) analyses the empirical settings of Koehn and Santomero (1980) and Kim and Santomero (1988) and criticizes the validity of their assumptions. In the case of the risk insensitive insurance premium the risk-taking behaviour increases of the banks if there are no capital requirements. Nevertheless, he also argues that when taking limited liability into account that capital requirements do not necessarily reduce the risk-taking behaviour of a bank. Lastly, Calem and Rob (1999) combine the empirical models of the researchers and conclude that

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12 the relationship between risk taking and capital regulation is U-shaped. Banks with low capitalization take excessive risks, so they can profit from the deposit insurance. And banks with high capitalization take excessive risks, so they can compensate for the lower expected return due the lower amount of leverage.

In financial markets, there are three types of risks that can be classified in the following broad categories: operational risk, market risk and credit risk. For a bank, it is important to deal with these risks. In the case of market risk, it is interesting for a bank to quantify the maximum loss that a bank may face given an extreme event. This maximum loss within the confidence interval can be calculated by using the Value-at-Risk (VaR). The VaR is adopted by the Basel Committee on Banking Supervision (BCBS, 2013) as financial risk measure to set up the capital regulations for banks. BCBS has chosen this measure, instead of standard financial risk measures as z-score or SDROA, because the VaR gives an outcome of the potential loss for a bank with a given probability over a specific time horizon (Tsay, 2010). From this perspective, regulators can interpret the VaR as the minimum loss related to a financial crisis.

The recent financial crisis showed the relevance of quantifying market risk, but has also emphasized the weaknesses of the current VaR. This measure does not consider the extreme events that occur in a financial crisis, which is the fat tail of the distribution. Therefore, new approaches have been developed to measure financial risk, such as the Expected Shortfall (ES). The ES can be viewed as an extension of the VaR and deals with the main drawback of this measure. The VaR gives no information on the potential loss once the confidence interval is exceeded. This problem is solved by the ES as can be seen below in figure 1. In 2013 BCBS has responded accordingly by replacing the VaR requirements by ES requirements. Another disadvantage of the VaR is that it implicitly assumes that the distributions are approximately symmetric around the mean. Lastly, ES is shown to be sub-additive, whereas VaR is not sub-additive6_{. Nonetheless, it must be considered that first the VaR has to be calculated before the} ES can be estimated.

Figure 1. ES describes the amount of loss to be expected when that loss has breached VaR for a given value of ∝.

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1.2 Related research

Demirguc-Kunt, Detragiache and Merrouche (2013) used a multicountry panel of banks to study whether better capitalized banks experienced higher stock returns during the financial crisis. This study uses 381 banks in 12 advanced economies during the period of 2005 to 2009. The authors used five types of capital ratios: Basel risk-adjusted ratio, the leverage ratio, the Tier 1 and Tier 2 ratios and the tangible equity ratio. They find that before the crisis differences in capital did not have a significant effect on stock returns. During the crisis, especially for high-capitalized banks a stronger relationship was found for performance and capital positions. Also, they found a more relevant relationship between leverage ratio and stock returns than for the risk-adjusted capital ratio.

Berger and Bouwman (2013) examine how capital affects a bank’s performance measured as market share and survival. The variable survival enters the regression as a dummy variable. The dummy variable equals one if the bank is in the sample one quarter before the crisis and is still in the sample one quarter after the crisis, and zero otherwise. Market share is the percentage change in a banks market share of aggregate gross total assets. The authors use a dataset of 60,589 banks in the US during the period of 1984 to 2010. The study uses one capital ratio, measured as the ratio of equity capital to total assets on survival and market share. The first finding is that capital helps small banks to increase their profitability and survival during market crisis, banking crisis and normal times. Further, they find that the equity capital ratio enhances the performance of medium and large banks primarily during the banking crisis.

Similarly, Estrella, Park & Peristiani (2002) examine the relationship between capital ratios and bank failure. The researchers used three types of capital ratios: risk-weighted capital ratio (Tier 1 ratio to risk-weighted ratio), leverage ratio (Tier 1 capital divided by total tangible assets) and the gross revenue ratio (Tier 1 capital divided by total interest and noninterest income before the deduction of any expense). The dataset includes all FDIC-insured commercial banks that failed or were in business between 1989 and 1993 which consist of 12,400 banks. This study concludes that all the three capital indicators are significant inversely related to bank failure. However, they find that risk-weighted capital ratios that are more complex are less relevant in explaining bank failure than a simpler ratio as a leverage ratio.

Beltratti & Stulz (2012) research the question what the possible causes are for the bad performing banks during the financial crisis. For examining this question, they used two capital ratios, namely: Tier 1 over risk-weighted assets and tangible equity over total assets. Performance is measured by the returns of the stocks. The research consists of 503 banks all over the world with a bias to US banks, given that the data is retrieved from Bankscope which is an US databank. The authors found that banks that were rewarded with large stock returns in 2006 are the banks whose stock suffered the largest losses during the crisis. Second, they find that stronger regulation does not lead to better performance of banks during the crisis. In general, the study finds out that banks in countries with stricter capital regulations experience higher stock returns.

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14 Finally, Vallascas and Keasey (2012) research which bank characteristics offer a shelter for systemic shocks and compare the relative effects of several prudential rules on a bank’s risk exposure. Stability is defined as the distance to default. The researchers of this study express the distance to default as the number of standard deviations that the market value of banks assets is above the default point by modelling bank equity as a call option on the market value of assets. The researchers use only one capital ratio. That is the Regulatory Capital divided by the risk-weighted assets. The sample includes 153 banks which are located in Europe. The findings show that also bank size, the share of non-interest income and asset growth which are not included in the Basel III Accord are important in explaining the bank’s risk exposure. The introduction of a cap on bank absolute size appears the most effective tool to reduce the distance to default. Furthermore, results show that regulatory capital seems not important in explaining the distance to default.

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CHAPTER 3 Data and sample size

3.1 Data

The databases Compustat and CRSP are used for this study. From CRSP the data related to stock prices are retrieved to compute the returns of the stocks, ES and VaR. All the other variables are retrieved from Compustat. This study consists of an U.S. bank sample. These databases are available at the University of Amsterdam in the library of the Roeterscomplex. The variables regressions are made with the use of MATLAB and Stata.

All companies with a SIC code between 6000 and 6300 will be downloaded in the period of Q3.2007 till Q4.2016. From this list banks with SIC code 6282 (investment advice) are excluded, because these are not in the lending business. Following Beltratti and Stulz (2012) for a financial institution to be in the sample as a deposit-taking bank, we require a loan to assets ratio above 10% and a deposit to assets ratio above 20%. Also, banks that have missing values on the capital ratios or financial stability measures are excluded. In the following step, only the banks are held in the sample that have 10 consecutive years of data on stock prices available. Equivalent to the research of Fama and French (1992), the sample is split into three quintiles. As the results of the study of Berger and Bouwman (2013) strongly suggest it is important to divide the data in subsamples based on assets. The researchers find a significant positive effect that capital regulation helps medium and large banks only during the crisis. However, for small banks it accounts that capital has a positive effect during the crisis and after the crisis. Also, Demirguc-Kunt, Detragiache & Merrouche (2013) stress that larger banks are less persistent to endure financial shocks. Hence, larger banks have a more complex balance sheet and are more opaque, they can artificially increase their capital ratios, for example by securitization. Consequently, these banks can imply that they have a less risky asset base than in reality. Lastly, all the variables in the sample have been winsorized 1% in each tail to control for the significant outliers. After the selection methods on the sample are applied the dataset is reduced from 1018 to 138 banks.

This study uses a variance inflation test (VIF) as an indicator of multicollinearity. Neter, Wasserman and Kutner (1989) state that researchers desire low levels of VIF. Given that, higher levels of VIF are known to affect adversely the results associated with a regression analysis. The researchers argue that a value below 10 is the maximum level of VIF. As displayed in APPENDIX B, all levels are below 10. Further, this study uses a Hausman test to test for model misspecification. This research consists of panel data over multiple years for banks, the Hausman test shows whether to use fixed or random effects for the model. The null hypothesis is that the preferred model has random effects and the alternate hypothesis is that the model has fixed effects. As can be seen in APPENDIX C, the preferred model is with fixed effects.

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16 Table 1. Summary statistics

Table 1 shows the summary statistics of this study. The crisis (cris) period has been defined as Q3.2007 – Q4.2009 and the non-crisis period as Q1.2010-Q4.2016. ES and VaR are calculated for each bank daily and then the quarterly averages are computed with an alpha of 5%. Tier 1 equals Tier 1 capital divided by risk-weighted assets. The standard deviation of Return on Assets (SDROA) is calculated for each bank in a given year. LIQrat is defined as Cash and Due from banks divided by Total Assets. Regulatory ratio (REG) is defined as sum of Tier 1 and Tier 2 capital divided by risk-weighted assets. CAR is defined as the common equity divided by total assets. DEPrat is defined as Total Deposits divided by Total Assets. PLLrat is defined as the Loan Losses for Provision divided by Total Assets. NLrat is defined as the Net Loans divided by Total Assets. LNat is a proxy for size of the bank and is defined as the natural logarithm of Total Assets.

Average Full Sample

Full Crisis After-crisis Observations Min

Lower Quantile Median Upper Quantile Max Standard Deviation ES -5.62 -8.75 -4.55 4946 -209.68 -6.22 -4.23 -3.35 -1.34 6.33 VaR -3.94 -6.16 -3.18 4946 -138.38 -4.37 -2.95 -2.37 -0.96 4.26 SDROA 0.13% 0.24% 0.09% 4943 0.00% 0.02% 0.04% 0.09% 3.40% 0.30% Tier 1 12.84% 11.37% 13.34% 4946 0.50% 10.85% 12.42% 14.30% 36.33% 3.11% REG 15.38% 14.01% 15.85% 4946 0.90% 12.93% 14.50% 16.45% 67.51% 4.51% CAR 10.32% 9.33% 10.66% 4946 -1.64% 8.60% 10.09% 11.92% 33.46% 3.22% LIQrat 4.81% 3.92% 5.11% 4946 0.13% 1.89% 2.94% 5.67% 44.00% 5.49% DEPrat 74.36% 70.43% 75.69% 4946 20.77% 69.66% 76.06% 80.87% 92.89% 9.12% NLrat 58.16% 61.03% 57.17% 22267 _12.37% _49.85% _63.07% _69.13% _82.22% _14.51% PLLrat 0.32% 0.58% 0.23% 4702 -0.98% 0.04% 0.13% 0.34% 7.16% 0.57% AT _{104339.20 85247.85 110851.40} 4946 814.80 3511.39 7098.32 19022.10 2577148.00 347448.00 LNat 9.34 9.13 9.41 4946 6.70 8.16 8.87 9.85 14.76 1.70

7_{Sharp decline in observations in comparison with the other variables. WRDS expanded the bank coverage in the late 90s to include mid and smaller market cap banks. To}

facilitate that expansion, WRDS created and established a streamlined collection template for the newly added companies. This was primarily done due to the lower breadth of data traditionally reported by the smaller market cap banks. As such, if there was no direct lease financing then it implied no LNDLFQ (“NLrat”).

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3.2 Data description

In table 1 an overview is given of the data of this study. The overview provides data on the stability measures, the capital ratios and control variables over the full time-, crisis- and after-crisis period. The stability measures ES and VaR are both lower in times of the crisis period. The mean of the ES in the crisis is -8.75%, this implies the expected return on the stock of the bank in the worst 5% scenarios. The mean of the VaR is -6.16% during the crisis. This return is the maximum loss that will not be exceeded with a given probability of 95%, which is defined as the confidence level in this research. It makes sense that the loss of the ES denotes higher than the VaR, since this measure calculates the potential loss once the confidence interval of the VaR is exceeded. Figure 2 illustrates the returns, ES and VaR for the Bank of America that is included in this dataset. The figure displays that the ES and VaR are below the daily returns of the stock of the Bank of America. Again, it makes sense that the ES is below VaR, since the ES calculates the expected loss in the tail of the VaR.

Figure 2. The daily returns of the stock of the Bank of America (BoA), ES and VaR during Q3.2007till Q.42016

The same effect is displayed in figure 3, where the average of the ES and the VaR of the 138 banks in the sample are given. Also, the volatility of the returns in both figures have the same trend. During the crisis period the volatility shows a sharp increase illustrated in figure 2, which results in larger losses displayed in figure 3 in that period. The same effect accounts to a less extent for Black Monday on 8 August 2011. After that period, the figure shows more stable returns.

Figure 3. Average of ES and VaR for all 138 banks during Q3.2007 till Q4.2016

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18 The mean of the SDROA during the crisis is 0.24% opposed to 0.09% during the after-crisis period. Also, the volatility of the Return on Assets (ROA) is higher in times of the financial crisis in comparison through the full period.

The impact of the financial crisis on the stability measures are also applicable on the capital measures. It can be roughly stated that most banks comply with the Basel III requirements. The mean of the Tier 1 ratio of 11.37% during the crisis is higher as compared to the required 5.0%. Also, the lower quintile of the Tier 1 ratio denotes a value of 10.85%, which is still higher than the required ratio. This also applies for the Regulatory capital ratio, where the mean during the crisis period exceeds the requirement of the Basel Accords, respectively with 14.01% against 11.5%. This is displayed in figure 4 that shows the average of the Tier 1 ratio, Regulatory ratio and CAR of all banks. In addition, the long dashed lines of the capital requirements are displayed for the Tier 1 and Regulatory capital in the same color. It is obviously that the average of the capital ratios exceed the minimum requirements. So, in general, the stability measures and capital ratios are decreasing during the crisis due the negative financial impact and in the period after the crisis the measures and ratios are increasing again.

Figure 4. Average of the bank’s capital ratios over time

Furthermore, table 1 presents the control variables. The Liquidity ratio and Deposits ratio are both decreasing in times of crisis, because these assets can be sold quickly in times of unexpected losses. Also, the Provision for Loan Losses has increased during the crisis. During the crisis, the probability of default on paying the loans increases, which results in an increase of the amount of Provision for Loan Losses. Further, we can see an increase in the Net Loans during the crisis. In addition, the amount of Assets decrease in times of the crisis. This is due the fact that banks use assets to persist financial shocks. Lastly, the stability of the 138 banks are given in a scatterplots below in figure 5 for the ES, VaR and SDROA. Each row represents one stability measure. The stability measures are divided in three charts; the first one displays all the banks through the period, the second one displays the 50% banks with the highest Tier 1 capital and the third chart displays the 50% banks with the lowest Tier 1

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19 capital. For all of the three stability measures the same trend can be seen in the figure 5. During the crisis the expected losses are larger and more volatile in comparison with the period after the crisis. In the period after the crisis there are still large losses, but these dots are outliers. The figures display obviously that on average the losses declined after the crisis. In row 2 in comparison to row 3 it can be noted again that the losses for the ES are larger than for the VaR. Chart 2 and 3 in the rows represent respectively the highest 50% and the lowest 50% Tier 1 in the sample. It shows that the volatility and losses for the lowest 50% in the sample are larger than for the highest 50% for all stability measures. This may implicate that banks with higher capital are more stable.

Figure 5. Scatterplots of the stability over time for the Tier 1 capital

Figure 5 shows a scatterplot of the data on each stability measures. In the first row, second row and third row are the ES, VaR and SDROA each respectively given. The first chart in each row is a two-way plot of a stability measures on year for all 138 banks. The second chart is a two-way plot of a stability measure for the highest 50% Tier 1 capital banks in the sample on year. The third chart is a two-way plot of a stability measure for the lowest 50% Tier 1 capital banks in the sample on year.

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20

CHAPTER 4 Methodology

This chapter describes the methodology of the research. We start with the regression that is used throughout this study. Thereafter, the computation of each financial stability measure is explained. After that, the estimation of the capital ratios are described. As last, the control variables are explained and their expected positive or negative impact on the stability measures. Based on the model of Demirguc-Kunt, Detragiache and Merrouche (2013) the following equation will be used to answer the research question:

𝑦

_𝑖𝑡

= ∝

_𝑖𝑡

+ 𝛽

₁

∗ 𝑘

_𝑖𝑡−1

+ 𝛽

₂

∗ (𝑑

_{𝑐𝑟𝑖𝑠𝑖𝑠}

∗ 𝑘

_𝑖𝑡−1

) + 𝛽

3

𝑑

𝑐𝑟𝑖𝑠𝑖𝑠

+ 𝛽

4

∗ 𝐿𝐼𝑄𝑟𝑎𝑡

𝑖𝑡−1

+ 𝛽

5

∗ 𝐷𝐸𝑃𝑟𝑎𝑡

_𝑖𝑡−1

+ 𝛽

₆

∗ 𝑁𝐿𝑟𝑎𝑡

_𝑖𝑡−1

+ 𝛽

₇

∗ 𝑃𝐿𝐿𝑟𝑎𝑡

_𝑖𝑡−1

+ 𝛽

₈

∗ 𝐿𝑁𝑎𝑡

_𝑖𝑡−1

+ 𝛽

₁₀

∗ 𝐿𝑁𝑎𝑡

𝑖𝑡−1

∗ 𝑘

𝑖𝑡−1

+ 𝛽

11

∗ 𝐿𝑁𝑎𝑡

𝑖𝑡−1

∗ 𝑘

𝑖𝑡−1

∗ 𝑑

𝑐𝑟𝑖𝑠𝑖𝑠

+ 𝑢

𝑖𝑡

, where

𝑦

_𝑖𝑡

stands for the stability measures,

𝑘

_𝑖𝑡−1

stands for the capital ratios,

𝑑

_{𝑐𝑟𝑖𝑠𝑖𝑠}

is a

dummy variable for the crisis, 𝐿𝐼𝑄𝑟𝑎𝑡

_𝑖𝑡−1

is the liquidity ratio, 𝐷𝐸𝑃𝑟𝑎𝑡

_𝑖𝑡−1

is the deposit ratio,

𝑁𝐿𝑟𝑎𝑡

𝑖𝑡−1

is the net loan ratio and 𝐿𝑁𝑎𝑡

𝑖𝑡−1

is the natural logarithm of total assets.

The parameters ∝𝑗𝑡 , 𝛽𝑥 and 𝑢𝑖𝑡 are estimated using robust standard errors to account for the heteroscedasticity. By using lagged values of the capital ratios (and control variables), it is ensured that changes are incorporated in the stability measures. Also, year fixed effects are included to capture the influence of aggregate time series trends. Further firm fixed effects are included to control for omitted variables that differ between firms but that are constant over time. The dependent variable 𝑦_𝑖𝑡 refers to stability for each company i and quarter t.

This study uses the following stability measures: ES, VaR, SDROA. The first model that is used to calculate the VaR is the RiskMetrics TM model computed by J.P. Morgan in 1995 (Tsay, 2001). In the RiskMetrics TM model, the stock returns are assumed to have a conditional normal distribution with mean zero and a time varying variance, expressed as Exponentially Weighted Moving Average (EWMA). Due to several shortcomings of the EWMA model, different lines of research have originated in the field of modelling the volatility and VaR of asset returns. As of today, the GARCH type models of Engle (1982) have been widely used for this purpose. This study uses the approach of Engle and Patton (2001) and takes a GARCH (1,1) model to estimate the conditional volatility and follow So and Yu (2006) to calculate the one-step-ahead VaR. This boils down to the following model:

𝑟

𝑡

= 𝜇 + 𝑎

𝑡

,

𝑎

𝑡

= 𝜎

𝑡

𝜖

𝑡

,

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21

𝜎

_𝑡2

= 𝛼

0

+ 𝛼

1

𝑎

𝑡−12

+ 𝛽

1

𝜎

𝑡−12

,

where rt is the return at time t, μ is the time-invariant mean of the asset returns and where the innovation are Student-t distributed with ν degrees of freedom, i.e.:

𝜖

_𝑡

∼ 𝑡

_𝜈

, the GARCH(1,1) are estimated by Matlab via the GARCH toolbox based on maximum likelihood. Once all the parameters have been estimated, one can use the underlying distribution of the asset returns to calculate the VaR (see Tsay, 2001; So and Yu, 2006).

That is, the α% one-step-ahead VaR, defined as:

VaR

𝑡+1,𝛼

= 𝜇̂ + 𝜃

1−𝛼

𝜎̂

𝑡+1

, where

𝜎̂

𝑡+1 is the predicted one-step-ahead conditional variance and

𝜃

1−𝛼 is the quantile of the estimated Student-t distribution with ν degrees is freedom that is used for the VaR modelling. This study follow Tsay (2001) to calculate the α% one-step-ahead ES as:

𝐸𝑆

_𝑡,𝛼

= 𝜇̂ + √

𝜈̂ − 2

𝜈̂

𝑔

_𝜈_̂

(𝑡

_𝜈_̂−1

(𝛼))

1 − 𝛼

𝜈 + (𝑡

_𝜈_̂−1

(𝛼))

2

𝜈̂ − 1

𝜎̂

𝑡+1

,

, where 𝑔_𝑣

(⋅) is the density function of the Student- t distribution and 𝑡

𝑣 the distribution function of the Student- t distribution with ν degrees of freedom. Note that, since quarterly data is used in this panel, the one-step-ahead ES and VaR forecasts are aggregated and averages are obtained for the quarterly VaR and ES. If quarterly one step ahead ES and VaR were used, then the estimations would be more biased. Given that, less of the variance of the stock prices in this manner are explained. The standard deviation of return on assets is the third measure for stability. This measure is calculated by the annually computation based on the four quarters in the current year. The lagged variable,

𝑘

_𝑖𝑡−1, is the most important independent variable. It refers to the capital ratios. In this study, there will be used three different measures of bank capital. The first capital ratio is core Tier 1 capital ratio and is defined following the Basel Accord rules as:

𝑇𝑖𝑒𝑟 1 =

𝑐𝑜𝑟𝑒 𝑇𝑖𝑒𝑟 1

𝑅𝑖𝑠𝑘 − 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠

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22 Basel III framework as:

𝑅𝐸𝐺 =

𝑐𝑜𝑟𝑒 𝑇𝑖𝑒𝑟 1 + 𝑇𝑖𝑒𝑟 2

𝑅𝑖𝑠𝑘 − 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠

Tier 1 is the bank’s core capital and is considered less risky. It contains of equity and retained earnings and can be used to absorb financial shocks that result in unexpected losses. Tier 2 is a bank’s supplementary capital (BCBS, 2011). The risk-weighted assets are the bank’s exposure to risk. Each specific asset of the bank belongs to a certain factor of risk. In this manner, it provides an easier tool for the BCBS to compare the risks of banks with each other. In addition, also off balance-sheet exposures can be easily included (BCBS, 2011). Further, the Basel Committee can make a distinction between illiquid assets (e.g. infrastructure investment) and less risky liquid assets (e.g. short-term loans). Lastly, the Capital Asset Ratio, which is defined as a simple capital ratio, is tested on the stability measures. This ratio is defined as total common equity dived by total assets. Estrella, Park & Peristiani (2000) find that simpler ratios are better in explaining bank failure, hence risk weighted capital ratios allow banks to artificially increase their capital by manipulating their accounting practices.

The first control variable is liquidity defined as cash and due from banks divided by total assets. Demirguc-Kunt, Detragiache and Merrouche (2013) included liquidity in the model, hence liquid assets can be sold quickly. Therefore, banks with a higher liquidity are better able to deal with unexpected losses. Hereafter comes, deposits which is divided by total assets. In this study, a positive relation is expected between deposits and stability. Berger and Bouwman (2013) stressed that banks with a higher deposit ratio were more stable during the crises, because banks with more and more sources of funding had more to chance to survive. They also stress that if banks had more retail deposits they had more chance to survive, because retail deposits where less sensitive to bank runs than wholesale deposits. The third control variable is the net loans to total assets. This control variable affects the credit risk of a bank. Therefore Demirguc-Kunt, Detragiache and Merrouche (2013) expect a negative relationship to the financial stability of a bank. The following control variable is the loan loss provision divided by total assets. Banks with a higher amount of loan loss failure are expected to have a higher chance of insolvency. Therefore, Berger and Bouwman (2013) expect a negative relation for provision of loan losses and stability. Lastly, this study controls for size. The variable is defined as the log of total assets, because than it is more likely that the distribution is more normal. The relationship for size and stability is ambiguous. Berger and Bouwman (2013) argue that a bank with higher level of assets is better resistant against a financial shock. Because of higher level of assets, these banks are better able to diversify their assets and gain from economies of scale. Further, large banks have the advantage of too big to fail support of governments. In contrast with the findings of Berger and Bouwman (2013), the authors Micco, Panizza, and Yanez (2007) find no significant relationship between the size and the profitability of a bank. Berger and Bouwman (2013) stressed that banks that are too-big-to-fail do not

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23 profit of higher capitalization due the support of the government if the banks suffer in a downturn period. A short overview of the variables and the expected signs are given below in table 2.

Table 2. Key variable expectations

This table lists all key variables and expected sign according to the regressions in this research with a brief explanation. Tier 1 equals Tier 1 capital divided by risk-weighted assets. The standard deviation of Return on Assets (SDROA) is calculated for each bank in a given year. LIQrat is defined as Cash and Due from banks divided by Total Assets. Regulatory ratio (REG) is defined as sum of Tier 1 and Tier 2 capital divided by risk-weighted assets. CAR is defined as the common equity divided by total assets. DEPrat is defined as Total Deposits divided by Total Assets. PLLrat is defined as the Loan Losses for Provision divided by Total Assets. NLrat is defined as the Net Loans divided by Total Assets. LNat is a proxy for size of the bank and is defined as the natural logarithm of Total Assets.

Variable Expected Sign Interpretation

Tier 1 capital + Buffer against unexpected losses Regulatory capital + Buffer against unexpected losses

CAR + Buffer against unexpected losses

LIQrat - Liquid assets can be sold quickly

DEPrat - More sources of funding, more chance to survive

NLrat - The credit risk of a bank

PLLrat - High chance of insolvency

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24

CHAPTER 5 Results

Multiple regression analyses are done to estimate the effect of different capital ratios on bank stability. The capital ratios; Tier 1, Regulatory and CAR are each tested separately on ES. In each model are 12 different regressions included which show the effect if control variables, interaction terms, year and firm fixed effects are added. The tables 3, 4 and 5 that belong respectively to section 5.1-5.3 are given directly below section 5.3.

5.1 Effect of Tier 1 capital ratio on the Expected Shortfall

Table 3 shows the regressions of Tier 1 on the ES. In the model, it can be seen that Tier 1 has a significant positive effect on the ES. This effect stays significant when crisis and the interaction term Tier 1 and crisis are added in regressions 2, 6 and 10. The dummy crisis has a negative impact on the ES through the model. This effect becomes clear in figure 3, where you can see that the ES is significantly lower during the crisis. The interaction term Tier 1 and crisis is as unexpected insignificant in these regressions. However, this changes when control variables are added to the model. Due the added control variables the Tier 1 becomes insignificant and Tier 1 during the crisis becomes significant. This is in line with the results of Demirguc-Kunt, Detragiache and Merrouche (2013) and Berger and Bouwman (2013) that capital helps primarily during the crisis. The signs of the added control variables are overall as expected. Nonetheless, in regressions 3 and 4 LIQrat shows a surprising negative impact on the ES. Given that, liquid assets can be sold quickly and therefore banks with higher liquidity are better able to deal with unexpected losses a positive relationship would be expected. A possible explanation for the negative effect could be that the ES is derived from the stock prices. So, from an equity shareholder perspective, a bank can be seen as ineffective due the fact that the bank holds relative expensive liquid assets, whereas the bank earns it highest return on loans. Further, this term becomes insignificant when the year and firm fixed effects are added to the model. This leads to an increase of the Adj. R-squared to 44%, which might therefore a better model than the first four regressions. Also, the negative significant impact of LNat on the ES is not as expected in regression 7. However, like the explanation for LIQrat, this significant effect disappears when year fixed effects are added to the model. In all the regressions Provision for Loan Losses show a significant large impact. This large effect is as expected, since banks with a higher expected amount of loan loss failure have a higher chance of insolvency. In regressions 4, 8 and 12 the interaction term of Tier 1 and assets during the crisis shows a negative impact on the ES. This implicates that when banks are of larger scale it has a negative stabilizing effect. This effect is counterintuitive, given that, these larger banks are better able to diversify their assets and gain from economies of scale. However, from an equity perspective, investors may think that larger banks that have a more complex balance sheet are able to artificially increase their capital ratios, for example by securitization. In addition, this effect is in line with the theory of the U-shape of Demirguc-Kunt, Detragiache and Merrouche (2013). For these kind of banks, the benefits of capital do not hold, since

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25 these banks know they will be supported if needed (Berger and Bouwman, 2013). Therefore, this counterintuitive effect might be driven by the inclusion of these very large institutions. In chapter 6, this study controls for this effect by running the regressions again without the inclusion of very large institutions. Overall, regression 12 has the highest Adj. R-squared of the model when the year and fixed effects are included. The regression explains 44.4% of the variability of the ES around its mean.

5.2 Effect of Regulatory capital ratio on the Expected Shortfall

The model in table 4 shows the results of the Regulatory capital ratio on the ES. The Regulatory capital shows in several ways the same results as the Tier 1 ratio on the ES. Only in regressions 3 and 7 the capital shows a significant negative effect on the ES. The Regulatory capital consists of core Tier 1 and the supplementary capital Tier 2. The correlation table 14, APPENDIX D, shows that Tier 2 capital has a positive correlation with the ES. Therefore, it is counterintuitive that the capital has a negative impact on the ES, given that both variables have a positive correlation with the ES. Nonetheless, in the model with the highest Adj. R-squared with more than 44% the capital ratio shows an insignificant relationship. The last regression 12, the one with the highest Adj. R-squared, shows uniform results as regression 12 in table 3. Regulatory capital has a positive impact during the crisis. Again, Provision for Loan Losses is the only significant control variable and has a large negative impact on the ES. Lastly, the interaction term Regulatory capital and assets during the crisis has again a negative impact on the ES.

5.3 Effect of Capital Asset Ratio on the Expected Shortfall

Table 5 shows the effect of CAR on the ES. In contrast to the Tier 1 and Regulatory ratio, it presents no uniform results. When the CAR is solely regressed on ES, it shows a positive relationship with the ES. This implicates that on average an increase in the CAR ratio has a positive effect on the ES. However, when the control variables are added to the model the capital ratio shows no significant relationship anymore. Therefore, it can be stated that CAR, which is a simple capital ratio, is not better in explaining the financial stability of a bank than a complex risk-weighted capital ratio. Therefore, the outcomes of these regression are in line with the results of Kim and Santomero (1988). They find that risk-weighted capital ratios are better in explaining the financial stability of banks in comparison to simpler capital ratios.

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26

Table 3. Regressions of Tier 1 ratio on ES.

Table 3 presents the results of the regression of Tier 1 ratio (Tier 1) on ES. The crisis (cris) period has been defined as Q3.2007 – Q4.2009. ES is calculated for each bank daily and then the quarterly averages are computed with an alpha of 5%. Tier 1 equals Tier 1 capital divided by risk-weighted assets. DEPrat is defined as Total Deposits divided by Total Assets. PLLrat is defined as the Loan Losses for Provision divided by Total Assets. NLrat is defined as the Net Loans divided by Total Assets. LNat is defined as the natural logarithm of Total Assets. For all the regressions are robust standard errors applied.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) ES ES ES ES ES ES ES ES ES ES ES ES Tier 1 0.298*** 0.124** -0.307 0.664 0.614*** 0.338** 0.245 0.471 0.375*** 0.386*** -0.131 0.671 (0.0404) (0.0551) (0.277) (0.464) (0.103) (0.135) (0.226) (0.687) (0.124) (0.136) (0.0799) (0.470) Tier 1*cris 0.0773 0.344* 1.018*** -0.122 0.136 0.783*** -0.0614 0.325*** 0.814*** (0.0734) (0.193) (0.270) (0.0896) (0.117) (0.227) (0.0881) (0.0966) (0.195) Cris -5.113*** -8.635*** -7.286*** -2.382* -6.431*** -3.911** -0.798 -5.644*** -4.045*** (0.999) (2.164) (2.414) (1.306) (1.309) (1.582) (1.089) (1.300) (1.450) LIQrat -6.139*** -5.087*** 4.316 2.012 4.595 3.560 (1.722) (1.859) (5.871) (6.195) (3.375) (3.578) DEPrat 4.474*** 4.558*** 10.13*** 11.57*** 1.643 1.929 (1.341) (1.354) (2.850) (3.206) (3.513) (3.568) NLrat -6.384*** -6.170*** -5.148 -5.703 -3.808 -4.242 (1.619) (1.548) (3.492) (3.389) (3.563) (3.342) PLLrat -153.9*** -143.6*** -86.21*** -74.95*** -86.62** -74.98** (28.34) (28.42) (21.53) (18.58) (37.07) (33.67) LNat -0.0633 1.189** -1.647** -0.904 -2.371 -1.729 (0.0832) (0.601) (0.716) (1.149) (2.111) (1.104) Tier 1*LNat -0.0917* -0.0600 -0.0703 (0.0507) (0.0675) (0.0452) Tier 1*LNat*cris -0.0755*** -0.0811*** -0.0632*** (0.0249) (0.0272) (0.0211) Constant -9.441*** -6.199*** 1.640 -12.04** -13.49*** -9.061*** 12.74 3.180 -9.921*** -8.606*** 25.59 18.32 (0.576) (0.810) (3.309) (5.760) (1.325) (1.813) (8.081) (12.04) (1.270) (1.611) (16.02) (15.45) Observations 4,809 4,809 2,183 2,183 4,809 4,809 2,183 2,183 4,809 4,809 2,183 2,183 Adj. R-squared 0.021 0.093 0.266 0.274 0.049 0.107 0.243 0.252 0.214 0.214 0.439 0.444

Year Fixed Effects No No No No No No No No Yes Yes Yes Yes

Firm Fixed Effects No No No No Yes Yes Yes Yes Yes Yes Yes Yes

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

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27

Table 4. Regressions of Regulatory ratio on ES.

Table 4 shows the estimated coefficients of the regression of Regulatory ratio (REG) on ES. The crisis (cris) period has been defined as Q3.2007 – Q4.2009. ES is calculated for each bank daily and then the quarterly averages are computed with an alpha of 5%. Regulatory ratio is defined as sum of Tier 1 and Tier 2 capital divided by risk-weighted assets. LIQrat is defined as Cash and Due from banks divided by Total Assets. DEPrat is defined as Total Deposits divided by Total Assets. PLLrat is defined as the Loan Losses for Provision divided by Total Assets. NLrat is defined as the Net Loans divided by Total Assets. LNat is defined as the natural logarithm of Total Assets. For all the regressions are robust standard errors applied.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) ES ES ES ES ES ES ES ES ES ES ES ES REG 0.168*** 0.0791*** -0.236** 0.953** 0.437*** 0.224** -0.153** 0.666 0.287*** 0.293** 0.0251 0.814 (0.0231) (0.0297) (0.110) (0.444) (0.0950) (0.104) (0.0640) (0.734) (0.0998) (0.113) (0.0623) (0.504) REG*cris 0.0649* 0.206 0.838*** -0.0353 -0.0386 0.561*** -0.0265 -0.00469 0.502*** (0.0377) (0.173) (0.213) (0.0620) (0.147) (0.170) (0.0650) (0.115) (0.152) Cris -5.244*** -7.531*** -7.100*** -3.544*** -4.260** -3.573* -1.351 -2.340 -1.763 (0.656) (2.311) (2.185) (1.067) (2.032) (1.962) (0.971) (1.556) (1.453) LIQrat -5.714*** -5.482*** 4.371 1.014 4.961 2.181 (1.706) (1.769) (5.743) (5.829) (3.403) (3.747) DEPrat 3.901*** 3.223** 9.500*** 10.12*** 1.216 1.275 (1.316) (1.389) (2.827) (3.062) (3.471) (3.477) NLrat -5.431*** -5.490*** -4.853 -5.610* -3.285 -3.965 (1.273) (1.279) (3.445) (3.268) (3.516) (3.170) PLLrat -154.0*** -138.7*** -81.35*** -69.65*** -90.44** -75.70** (28.57) (28.74) (21.44) (18.10) (38.49) (34.97) LNat -0.00263 1.789*** -1.648** -0.594 -2.388** -1.504 (0.0653) (0.623) (0.755) (1.331) (1.077) (1.187) REG*LNat -0.114*** -0.0762 -0.0733 (0.0428) (0.0702) (0.0482) REG*LNat*cris -0.0623*** -0.0604*** -0.0528*** (0.0172) (0.0166) (0.0137) Constant -8.202*** -5.803*** 0.438 -17.92*** -12.34*** -8.105*** 12.21 1.047 -9.738*** -8.129*** 23.89 14.95 (0.410) (0.546) (2.486) (6.408) (1.464) (1.665) (8.670) (13.61) (1.267) (1.574) (15.18) (15.47) Observations 4,809 4,809 2,183 2,183 4,809 4,809 2,183 2,183 4,809 4,809 2,183 2,183 Adj. R-squared 0.014 0.093 0.263 0.274 0.033 0.103 0.243 0.253 0.211 0.211 0.436 0.444

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28

Table 5. Regressions of CAR ratio on ES.

Table 5 shows the estimated coefficients of the regression of CAR ratio (CAR) on ES. The crisis (cris) period has been defined as Q3.2007 – Q4.2009. ES is calculated for each bank daily and then the quarterly averages are computed with an alpha of 5%. CAR is defined as common equity divided by total assets. LIQrat is defined as Cash and Due from banks divided by Total Assets. DEPrat is defined as Total Deposits divided by Total Assets. PLLrat is defined as the Loan Losses for Provision divided by Total Assets. NLrat is defined as the Net Loans divided by Total Assets. LNat is defined as the natural logarithm of Total Assets. For all the regressions are robust standard errors applied.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) ES ES ES ES ES ES ES ES ES ES ES ES CAR 38.64*** 29.42*** 5.103 100.0*** 85.57*** 61.64*** 4.623 -39.11 51.42*** 51.12*** -0.771 -39.47 -5.736 (6.534) (3.959) (22.27) (17.98) (18.28) (6.069) (53.43) (17.12) (17.52) (6.930) (49.38) CAR*cris 0.0206 -0.0521 -0.0262 -0.0184 -0.199 -0.145 0.0185 0.0221 0.0790 (0.0361) (0.142) (0.153) (0.0533) (0.155) (0.148) (0.0427) (0.113) (0.0989) Cris -4.419*** -3.601* -2.228 -3.502*** -1.790 -0.756 -1.644** -2.721** -1.675 (0.664) (1.888) (1.737) (0.888) (2.063) (2.705) (0.714) (1.171) (1.864) LIQrat -5.942*** -4.990*** 3.115 3.301 5.148 5.221 (1.690) (1.647) (5.608) (5.667) (3.411) (3.770) DEPrat 4.547*** 4.906*** 9.721*** 9.377*** 1.260 1.556 (1.325) (1.339) (3.120) (3.068) (3.664) (3.631) NLrat -5.218*** -5.015*** -4.148 -4.326 -3.390 -3.580 (1.237) (1.235) (3.270) (3.266) (3.530) (3.422) PLLrat -159.0*** -152.3*** -79.78*** -72.74*** -91.49** -85.14** (30.16) (29.78) (23.03) (23.42) (37.65) (36.62) LNat 0.0743 0.858*** -1.110 -1.652* -2.433** -2.736*** (0.0679) (0.198) (0.670) (0.838) (1.004) (0.703) CAR*LNat -8.059*** 5.266 4.695 (1.937) (4.745) (4.392) CAR*LNat*cris -1.693* -1.711 -1.535 (0.919) (1.702) (1.195) Constant -9.586*** -7.664*** -4.998*** -14.83*** -14.42*** -11.07*** 3.023 7.976 -10.96*** -9.528*** 24.84* 26.75** (0.662) (0.784) (1.611) (2.862) (1.851) (1.945) (6.533) (7.964) (1.623) (1.887) (13.69) (9.855) Observations 4,809 4,809 2,183 2,183 4,809 4,809 2,183 2,183 4,809 4,809 2,183 2,183 Adj. R-squared 0.038 0.111 0.258 0.263 0.063 0.126 0.242 0.245 0.219 0.219 0.436 0.438

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CHAPTER 6 Robustness checks

To test the results several robustness checks have been performed. The first robustness checks have been performed on the dependent variables. Before the ES was used as official financial stability measure the VaR was used as indicator by the Basel Committee. Therefore, the regressions have also been performed again on this variable. To expand this robustness check, this study controls also on the stability measure SDROA. Table 6 that belongs to respectively section 6.1 and 6.2 is given directly below section 6.28_.

6.1 Effect of capital ratios on the Value at Risk

The regressions 1, 2 and 3 in table 6 represent the results of respectively Tier 1, Regulatory Capital and CAR on the VaR. The regressions show similar results as the capital on the ES. An increase in the Tier 1 and Regulatory capital during the crisis have a positive effect on the ES, which results in a stabilizing impact on the banks. These complex risk-weighted ratios show no significant relationship with the ES over the whole period. However, both ratios have a negative significant effect on the ES when the banks are of larger scale during the crisis. This implies, that banks with larger assets have a negative impact on the stability during the crisis. The CAR shows no significant effects on the VaR as in line with the results of the CAR on the ES. This implicates again that the CAR is not better in explaining the stability of a bank. It can be concluded that the results are robust when the VaR is used as stability measure.

6.2 Effect of capital ratios on SDROA

The impact of the Tier 1 ratio, Regulatory ratio and CAR on the SDROA are respectively given in regression 4, 5 and 6 in table 6. The regressions show no similar results as the capital on the ES. In contrast to the ES, Tier 1 capital has no significant relationship with the SDROA. However, the Regulatory capital and CAR has a negative significant impact on the SDROA. A negative effect on the SDROA results in a stabilizing effect on the banks. When the regression control for the size of the banks none of the interaction terms show significant results. The capital ratios show no uniform results like the capital ratios on the ES. Therefore, it cannot be stated that these outcomes are robust.

8_{For simplicity, the control variables are left out of the table. This accounts also for the following tables after}

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Table 6. Regressions of capital ratios on stability measures VaR and SDROA

Table 6 shows the estimated coefficients of capital ratios: Tier 1, Regulatory and CAR on VaR in regression 1, 2 and 3 and on SDROA in regression 4, 5 and 6. Tier 1 equals Tier 1 capital divided by risk-weighted assets. Regulatory ratio is defined as sum of Tier 1 and Tier 2 capital divided by risk-weighted assets. CAR is defined as common equity divided by total assets. The crisis (cris) period has been defined as Q3.2007 – Q4.2009.

(1) (2) (3) (4) (5) (6)

VaR VaR VaR SDROA SDROA SDROA

Tier 1 0.515 0.000463 (0.310) (0.001) Tier 1*cris 0.494*** -0.00027 (0.144) (0.000) Tier 1*LNat -0.0538* 0.00003 (0.030) (0.000) Tier 1*LNat*cris -0.0348** -0.00008 (0.015) (0.000) REG 0.566 0.000382 (0.335) (0.001) REG*cris 0.305*** -0.000313* (0.110) (0.000) REG*LNat -0.0518 -0.00003 (0.032) (0.000) REG*LNat*cris _-0.0295*** -0.00002 (0.010) (0.000) CAR -17.44 -0.133 (33.840) (0.091) CAR*cris 0.0637 -0.000322* (0.068) (0.000) CAR*LNat 2.17 0.0131 (3.031) (0.009) CAR*LNat*cris -0.83 0.00197 (0.751) (0.002) Constant 5.38 -0.0295*** 11.84* -0.0259 -0.0235 -0.00893 (10.690) (0.010) (6.495) (0.021) (0.022) (0.010) Observations 2,183 2,183 2,183 2,183 2,183 2,183 Adj. R-squared 0.473 0.473 0.469 0.221 0.22 0.247

Constant Yes Yes Yes Yes Yes Yes

Control Variables Yes Yes Yes Yes Yes Yes

Year Fixed Effects Yes Yes Yes Yes Yes Yes

Firm Fixed Effects Yes Yes Yes Yes Yes Yes

Capital regulation and financial stability of banks : are regulators shaping the right framework to prevent a new banking crisis?