Capital ratios and bank stability

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Capital ratios and bank stability

Abstract

This study analyzes the effect of bank capital on bank stability during the global financial crisis of 2007. Bank stability is measured as standard deviation of return on assets and return on equity, and the z-score. Bank capital is measured as Tier 1 capital ratio, Tier 2 capital ratio, and the unweighted leverage ratio. The data used for the study consists of 4,564 observations, over 616 unique U.S. banks over the period 2004-2012. The results are as follows. i) Banks with a higher Tier 1 and Tier 2 capital ratio have more stable returns on assets and returns on equity and have a higher z-score during the crisis period. ii) The unweighted leverage ratio shows contradictive, and sometimes even volatility increasing results, which suggests that the unweighted leverage ratio is an inappropriate capital measure to limit volatility in returns. iii) Bank capital has a stronger stabilizing effect when banks are of larger scale. iv) When banks are separated by small, medium, and large size banks, and the sample period is reduced to only the pre-crisis and crisis period, results show that Tier 1 and Tier 2 capital only have a stabilizing effect on ROA and ROE for small size banks, and have no significant effect on medium and large banks. v) Additionally, when applying the z-score as stability measure, Tier 1 and Tier 2 capital ratio show stabilizing results for small banks at all time, and for medium and large banks primarily during the crisis.

Master Thesis

MSc Business Economics – Finance Track

Pieter Maas - 6344348 July 2016

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Statement of Originality

This document is written by Student Pieter Maas who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Acknowledgement

I would first like to thank my thesis advisor Mr. M.A. Dijkstra of the Faculty of Economics and Business at the University of Amsterdam. The door to Mr. Dijkstra’s office was always open whenever I ran into a trouble spot or had a question about my research or writing. He allowed this paper to be my own work, but steered me in the right the direction whenever he thought I needed it.

Second I would also like to thank my friends I met during my study time at the University of Amsterdam, who made it a pleasant time with unfailing support and continuous encouragement throughout my years of study and through the process of researching and writing this thesis.

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1. Introduction

The recent global financial crisis, as well the ones before, have made it clear that systemic risk in the financial system is a great concern. Financial distress of a large bank can rapidly spill over into other banks and cause a credit crunch, or a drop in asset prices (Admati et al., 2013). The failure of financial regulation is said to be one of the main reasons of the financial crisis (Vickers, 2016). In response to the latest crisis the Basel Committee on banking supervision introduced the Basel III framework. This framework requires more stringent capital measures for banks. This measure aims to improve the ability to absorb shocks arising from financial and economic distress, whatever the cause might be (BIS, 2011). This amount of regulatory capital can be divided in two tiers; Tier 1 capital, which represents the amount of core capital (among others common equity, preferred stocks, or retained earnings), and Tier 2 capital, which represents the amount of supplementary capital (among others loan loss reserves, subordinated debt, and convertible stock). However, the effectiveness of these capital standards is often discussed after its introduction. On the one hand, capital requirements provide an equity cushion, which would decrease the possibility of default due to negative shocks in asset value. But on the other hand, capital requirements have been accused for distortions to the banking sector. It is been accused that holding more equity is costly for banks, because investors expect high returns. Forcing banks to use more expensive equity increase their costs, and may lower the return on equity. To compensate for these lower returns, banks are encouraged to take more risk, which is in contrary with the regulator’s intention (Admati et al., 2013). VanHoose (2007) suggests that the decision of taking more risk due to more stringent capital requirements depends on the level of risk-aversion of banks and their managers. So capital regulation could make some banks safer, and some banks riskier depending on the level of risk-aversion of bank. This may lead to ambiguous results of capital regulation.

The aim of the thesis is to examine the following research question: Have higher

capitalized banks more stable performance when they absorb negative asset shocks? More

specific: Have banks with a higher Tier 1 ratio, Tier 2 ratio, or unweighted leverage ratio more

stable return of assets or return on equity or a higher z-score when they absorb negative asset shocks? The data used to research this question consists of U.S. bank financials from the period

of 2004-2012. The period of 2007-2009, the global financial crisis, is seen as the crisis period, in which banks experienced negative shocks in their asset value. The stability of bank performance is measured by the standard deviation of return on assets (henceforth ROA) and the standard deviation of return on equity (henceforth ROE). For robustness, bank capital is measured by three different ratios; Tier 1 capital ratio, Tier 2 capital ratio, and the unweighted leverage ratio (henceforth unweighted ratio). The expectation is that: Higher capitalized banks are better able

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to absorb negative asset shocks, which results in more stable performance. Moreover, banks with

a higher Tier 1 ratio, Tier 2 ratio, or unweighted ratio will have a lower standard deviation of return on assets and return on equity, and a higher z-score.

This research differentiates from previous papers in several aspects. First, in addition to Demirguc-Kunt et al. (2013) and Beltratti & Stulz (2012) it uses an extended period, which includes not only the pre-crisis period but also the post-crisis period as an additional benchmark. Secondly, Demirguc-Kunt et al. (2013) and Beltratti & Stulz (2012) analyze the stock returns as performance measure, but stock prices are highly speculative, especially during the crisis. Therefore, bank performance is measured in this paper as the standard deviation of ROA and ROE, and the z-score. Thirdly, three different measures of bank capital are examined to determine whether the mutual effects differ. Fourthly, this paper includes an interaction term of bank’s assets and capital, to see whether the size of a bank influences of effect of capital regulation. When empirical research proves that the set hypothesis does not hold, it claims that capital regulation does not fulfill its goal. In this way it contributes to the ongoing discussion of capital regulation. It also shows the mutual effects of the different capital measures, whether there is a different effect of holding a certain amount of core (Tier 1), core plus supplementary (Tier 2) capital, or unweighted capital. In this way it contributes to the discussion, which capital measure is the most effective in creating a more stable banking climate.

The results of the base regressions are as expected. Banks with a higher Tier 1 and Tier 2 capital ratio have, during the crisis period, more stable ROA and ROE and a higher z-score. This indicates that higher capitalized banks are better able to deal with negative shock in asset value, which is in line with the findings of Beltratti & Stulz (2012), and the set hypothesis. Additionally, higher capital ratios also have a stabilizing effect on returns during the non-crisis period. The unweighted ratio shows contradictive, and sometimes even volatility-increasing effects on bank stability. This suggests that the unweighted ratio is an inappropriate capital measure to limit volatility in returns. These findings are contrary to the ones of Demirguc-Kunt et al. (2013). An interaction term is included to show whether bank capital has a different influence on banks with a different size. Results show that a higher Tier 1 and Tier 2 capital ratio overall results in more stability when banks are of larger scale. During the crisis period there is no different stabilizing effect of bank capital when banks are of larger scale. The results are not as expected when banks are separated by small, medium, and large size banks, and the sample is reduced to only the pre-crisis and crisis period. Results show that Tier 1 and Tier 2 capital only has a stabilizing effect ROA and ROE for small size banks during the crisis, and has no significant effect on medium and large banks. Additionally, when applying the z-score as stability measure, Tier 1 and Tier 2 capital ratio show stabilizing results for small banks at all time, and for medium and large banks primarily during the crisis. The results on ROA and ROE stability

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6 | P a g e suggest that capital regulation does stabilize returns on average, but does not achieve its goal to limit systemic risk within the financial system. Systemic risk occurs when financial distress of a large bank spills over to other financial institutions. This paper shows that the effect of capital ratios on the return stability of large banks is not significant, which implies that capital regulation does not achieve its goal to limit systemic risk.

This paper proceeds as follows. Section 2 discusses the relevant literature regarding capital regulation. To start with, it gives a theoretical overview of capital regulation. Then the negative and positive effects of capital regulation are discussed, and recent empirical evidence. The hypothesis is formulated at the end of section 2. Section 3 describes the methodology, the model and its control variables, data selection, and shows the descriptive statistics. The results are shown in section 4. In section 5 several robustness checks are done. Section 6 concludes.

2. Literature review

The effect of capital regulation on bank performance shows a twofold. On one hand, capital regulation may limit risks. Capital can be seen as a buffer that absorbs losses and hence reduces the risk of insolvency (Demirguc-Kunt et al., 2013). On the other hand, higher financial regulation may lead to excessive risk-taking by banks instead of mitigating them. Banks that are not risk-averse will choose to invest in a more risky asset mix, creating a perverse effect of regulation in which the probability of default increases (VanHoose, 2007).

The idea behind capital regulation is to diminish the moral hazard problem created by deposit insurance and limited liability. Deposit insurance is a measure introduced by the government1_{, which guarantees that depositors are not subject to loss. It protects depositors, in}

full or in part from losses caused by bank’s inability to repay its debt. Due to deposit insurance, depositors have fewer incentives to monitor banks (Dewatripont & Tirole, 1993). That is, if the bank fails, the provider of deposit insurance bears the risk that the depositors otherwise would have born (Santos, 2001). The limited liability theory is legal concept that protects equity holders from personal losses due to their ownership interest in a company, even if the company fails. In case of default limited liability ensures that banks can only lose their equity position, even though the bank may owe billions to its creditors.

The downside of deposit insurance and limited liability is that it may increase the incentives of a bank’s risk-taking (Akerlof & Romer, 1993; Merton, 1977). With non-financial institutions, the excessive risk-taking problem is not so severe because overall leverage is much

1_{Federal Deposit Insurance: first introduced through the Federal Deposit Insurance}

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7 | P a g e lower than in comparison to financial institutions. The incentives to engage in excessive risk taking are generally much lower. More risky projects often have a higher yield and a higher probability of defaulting. When risky projects are undertaken, depositors do not participate in the possible high returns. By contrast, the bank’s shareholders benefit from the high returns, but do not bear any increased risk, due to limited liability (Admati et al., 2013). When a bank only holds a small amount of capital, the bank’s investment decisions can be distorted. That is, the bank’s owners have no incentive to take downside risks into account when there is a new potential investment, since the potential losses in case of default are borne by creditors or the deposit insurance provider. In other words, the internal asset risk is not fairly priced by depositors and equity holders, which may cause incentives for bank owners to encourage risk or gamble (Hellmann et al., 2000; Repullo, 2004; Myerson, 2014; Martynova, 2015).

An increase in the amount of equity may limit this problem. Capital regulation is among others based on minimal capital requirements. A bank’s capital position refers to its owners’ stake in the bank’s investments. This minimum amount of capital forces bank’s equity holders to have some skin in the game, which refers to the fact that equity holders will lose their capital position in case of default. A risk-averse bank would be willing to take less risk when more of its own capital is at stake. Ex-ante, higher capitalized banks have higher potential losses in case of default, this reduces the incentives to take risk (Holmstrom & Tirole, 1997; Perotti et al., 2011). Additionally, an increase in capital enhances the bank’s ability to sustain negative shock in asset values. This decreases the probability of default, and it also lowers the costs when a default occurs, since a larger portion of losses would be absorbed by the bank’s equity (Admati et al., 2013).

2.1 Negative effects of capital regulation

Koehn & Santomero (1980) examine the effect of a bank’s portfolio allocation and risk to an increase in minimum capital asset ratio. Their model simulates a bank’s decision by using a simulated mean-variance portfolio selection model. The model examines the portfolio response of a bank, when it faces a regulatory change and estimates the optimal portfolio in respect to maximize the end-of-period capital, which is based on the bank’s risk aversion. Their simulations show that a bank that is sufficiently non risk-averse will respond to a stricter capital ratio by choosing a riskier portfolio allocation than before the increase in capital ratio. Their models shows, if regulators impose higher capital ratios, and the bank settles for the same risk-return trade-off in its portfolio as initially, the bank reallocates its portfolio towards assets with relatively higher risk and return. The reaction of the bank can be explained in two different ways. Firstly, the increase of the capital ratio results in a decrease in the probability of failure. As response the bank reallocates its portfolio towards more risky assets, to increase the

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8 | P a g e probability of failure and to settle for the same risk trade-off as before the adjustment. It depends on the level of risk-aversion of the bank whether the overall probability of default increases or decreases after increasing the minimum regulatory amount of capital. If a bank is sufficiently risk-averse, then the movement towards riskier assets will be small. When a bank is not risk-averse, the movement towards riskier assets will be larger, and will increase the overall risk-taking. This is a perverse effect of capital regulation, which increases the probability of default.

Kim & Santomero (1988) suggest that the use of a uniform capital ratio in regulation is an ineffective resolution to lower the risk of default. A uniform capital ratio is for all financial institutions the same, and is based on the amount of assets, instead of the risk-based ratio, which is unique for every institution. Their reasoning is that the use of a uniform capital ratio ignores the individual banks’ different preference structures and allows banks to avoid the regulation by the usage of leverage or business risk. Banks may choose to allocate their assets to riskier ones (increase business risk), to offset the result of lower leverage (lower financial risk), such that banks avoid regulations. As effective resolution they introduce risk-based capital requirements, which determine the minimum required levels of bank capital depending on the riskiness of the assets. The optimal risk weight requirements depend on three factors: the expected return, their variance-covariance structure, and the upper bound on the allowable insolvency risk the regulators have in mind. With knowledge of these three factors, the maximum allowable expected return on equity capital can be determined. This takes the individual risk preference of banks into account, and creates in this way a specific capital ratio for each bank.

2.2 Positive effects of capital regulation

Furlong & Keeley (1989) analyze the theoretical effect of more stringent capital regulation on bank asset portfolio risk. Risk is measured by the standard deviation of the rate of return on assets. Their research shows that the willingness to take risk declines as banks capital increases. That is, they argue that banks with an equity value maximizing objective will not increase the riskiness of their assets with increased capital standards. As a result of shareholder limited liability and the deposit insurance, bank shareholders may gain from upside potential, but are restricted from downside risk. A higher level of capital, however, exposes the shareholders to more risk. So more stringent capital regulation will reduce the value of deposit insurance, and therefore reduce the incentive of risk-taking. Keeley & Furlong (1990) argue the mean-variance portfolio selection model, used by Koehn & Santomero (1980) and Kim & Santomero (1988), and show it does not support its claimed results, that more stringent capital regulation will increase asset risk and may increase bankruptcy risk. Controversially, they show that the

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9 | P a g e variance of returns is an inappropriate risk measure, because the effects of changes in the capital ratio on risk and return are not linear, but it is a skew distribution, due to the change in value of deposit insurance. Moreover, the net value of the deposit insurance increases as asset risk increases. Thus, it mischaracterizes the bank’s investment opportunity by not taking the value of deposit insurance into account.

Santos (1999) uses a principal-agent model that generates two moral hazard problems by the dependence of the project’s expected return on the agent’s effort, which is not observable. One problem exists between the bank and the provider of deposit insurance, the other between the bank and an entrepreneur that demands funds to finance an investment. The model generates two outcomes; one if there is no moral hazard, and one if there is moral hazard, and how stricter capital requirements may affect those contracts. He shows that stricter capital requirements result in a contract adjustment that takes into account higher costs of default, and higher costs of required capital. A bank’s capital structure is influenced by the existence of deposit insurance and capital regulation. An increase in the required minimum amount of capital reduces the bank’s incentive to increase risk, which is due to the combined increase in the value of equity what the banker has at stake in case of bankruptcy. In order to minimize its costs in case of failure, the bank adjusts the financing contract in a way that it motivates the entrepreneur to make the investment in a safe project. The model shows that an increase in capital regulation lower risk taken and improves bank’s stability.

Admati et al. (2013) examine various arguments that are made to support that there are social costs, instead of benefit, associated with an increase in capital regulation. They conclude that bank equity is not socially expensive, but ensures that higher capitalized banks suffer fewer distortions in lending decisions and have more stable performance. Due to their equity cushion, the probability of default declines. Additionally, equity requirements reduce the incentives of managers to undertake excessively risky investments. Managers and shareholders benefit from the high returns in the event of success but do not bear the downside risk, since they are protected by liability limited. Increasing the equity requirements decreases the motivation of risk-taking, since they have more skin in the game. This results in a more stable and sound banking sector, which leads to fewer bailouts, and in the end reduces the social costs.

2.3 Recent empirical research

Avery & Berger (1991) analyze the relation between risk-based capital standards and bank performance. Their sample includes data on U.S. banks from 1982 to 1989. Bank performance is measured by four different variables: net income ratio to total assets, standard deviation of net income, ratio of non-performing loans to total assets, and the ratio of net loan charge-offs to total assets. Risk-based capital is separated in three different subcategories, 20%, 50%, and

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10 | P a g e 100% weight on-balance sheet assets. They show that in all cases, banks with higher ratios of risk-weighted assets to total assets have poorer performance. Additionally, the degree to which banks fail to meet the Tier 1 and total capital standards is found to be a good predictor of future performance problems.

Calem & Rob (1999) introduce a dynamic bank portfolio model in which a bank can choose to allocate investments in risky or safe assets. Both the asset portfolio and the capital position vary over time, as result of the investment choices a bank makes, which creates a dynamic model. They use bank financials from U.S. banks for 1984-1993, to find a U-shaped relation between capital position (flat non-based minimum capital requirement) and risk-taking (portfolio choice between risky or safe assets). Banks that do not meet the minimum capital requirements, and are undercapitalized, increase the riskiness of their investments to benefit from the deposit insurance. When bank capital rises, risk-taking is more limited. As capital rises even more, banks tend to take more risk, because they can absorb possible negative shocks in asset value.

Laeven & Levine (2009) examine the relation between risk taking by banks and capital regulation, taking into account the bank’s corporate governance. The corporate governance is incorporated by a dummy that equals one if a large owner has a seat on the management board, otherwise zero. Bank risk taking is measured using the z-score, which equals the return on assets plus the capital asset ratio to the standard deviation of asset returns. The z-score is an indicator of a bank’s distance from insolvency. They use a multi-country data set, across 48 countries, consisting of 279 banks over the period 1996-2001. Their results show that the capital requirements have different effects on bank risk taking, depending on the bank’s ownership structure. Banks with more powerful owners who hold more than 10% of the voting rights tend to take higher risks, which is indicated by a lower z-score. Since large owners’ incentives towards risk-taking are shaped along with their incentives to convert bank assets to the personal benefit. Likewise, managers that have an equity holding position take higher risks than non-equity holding managers. Bank owners might seek compensation for their utility loss and activity restrictions (regulatory restriction to banks engaging in securities market activities, insurance activities, real estate activities, and the ownership of non-financial firms) from more stringent capital restrictions by increasing their risk. For widely held banks (no shareholder holds more than 10% of the voting rights) the results have the opposite effect. These results show that, ignoring ownership structure, capital regulation can have an erroneous effect.

Podpiera (2006) explores the relation between the quality of regulation and supervision and bank performance. The quality of regulation and supervision is measured by a compliance assessment with the Basel Core Principles panel data over 65 countries from 1998-2002. The outcomes of the assessments result in an index of the Basel Core Principles compliance. This

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11 | P a g e index is included in the model to explore whether compliance has any impact on bank performance. Bank performance is measured by nonperforming loans and net interest margin. That is, the ability of banks to collect the money they have lent, which can be interpreted as a measure of the efficiency of banking performance. Podpiera (2006) finds a negative relation between compliance and nonperforming loans and net interest margin, which indicates a positive impact of the Basel Core Principles on bank performance.

Beltratti & Stulz (2012) investigate the variation in bank performance during the financial crisis from 2007-2008, and why some banks performed worse than others. Their sample included 503 financial institutions with assets in excess of $10 billion. As bank performance measure they used, among others, the volatility of stock returns. That is, idiosyncratic volatility which is the annualized standard deviation of the residual of a regression of weekly returns. Beltratti & Stulz (2012) use two different variables as capital ratio; Tier 1, defined as the ratio of Tier 1 capital to the total value of risk-weighted assets; and tangible equity, defined as equity minus intangible assets divided by total assets. They find that financial institutions with more Tier 1 capital or tangible assets had higher and less volatile stock returns, and that that the more assets a bank has, the less volatile its stock returns are.

Demirguc-Kunt et al. (2013) look at absolute stock returns, instead of the variance. They suggest that before the crisis, differences in capital did not have much impact on stock returns, but during the crisis, a higher capital position resulted in higher stock returns. They use panel data of 313 banks in 12 countries during the period of 2005-2009. As capital ratio they use the Basel risk-adjusted ratio, the leverage ratio, the Tier 1 and Tier 2 ratios, and the tangible equity ratio. The Basel risk-adjusted ratio has to be at least 8% of the value of the bank’s risk-weighted assets. To determine a bank’s value of risk-weighted assets, different types of assets are weighted according to the level of risk that each type represents. They find that the effect of capital on stock returns during the crisis is more sensitive to the leverage ratio than the risk-based capital ratio. This may be because the risk-risk-based capital ratios under Basel rules are subject to manipulation or in any case not reflective of true risk in the case of large banks. Additionally, higher quality forms of capital such as Tier 1 capital and tangible equity were of greater impact than supplementary capital.

Berger & Bouwman (2013) analyze multiple crises between 1984-2010, including the financial crisis of 2007-2009. They use bank survival and market share as performance measure. Bank survival is a dummy that equals one if a bank is still in the sample, and thus survived the previous crisis. Market share defined as the bank’s percentage change in market share (gross total assets to total industry’s gross total assets). As bank capital they use the equity capital ratio, measured as equity capital as a proportion of gross total assets. They show that survival and performance of small banks is positively impacted by capital in both crises and

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12 | P a g e normal times, but for medium and large banks, capital primarily helps during crises. Their sample consists of 57,243 small-bank, 1,946 medium-bank, and 1,400 large-bank observations. In contrast to previously discussed literature, Berger & Bouwman (2013) only use one main independent variable; the bank’s capital ratio, which is measured as the ratio of equity capital to gross total assets, averaged over the eight quarters before crises or normal time periods.

3. Methodology and data

3.1 Model

For the estimation of the effect of bank capital on bank stability, the model of Demirguc-Kunt et al. (2013) is used. The various estimations are made with the following equation:

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡= ∝𝑡𝑡+ 𝛽𝛽1∗ 𝐾𝐾𝑖𝑖,𝑡𝑡−1+ 𝛽𝛽2�𝐷𝐷𝑐𝑐𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑠𝑠𝑡𝑡∗ 𝐾𝐾𝑖𝑖,𝑡𝑡−1� + 𝐷𝐷𝑐𝑐𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑠𝑠𝑡𝑡+ 𝛾𝛾1∗ 𝐶𝐶𝐷𝐷𝑖𝑖,𝑡𝑡−1+ 𝛾𝛾2∗ 𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖,𝑡𝑡−1 + 𝛾𝛾3∗ 𝐿𝐿𝐿𝐿𝐷𝐷𝑖𝑖,𝑡𝑡−1+ 𝛾𝛾4∗ 𝑁𝑁𝐿𝐿𝑖𝑖,𝑡𝑡−1+ 𝛾𝛾5∗ 𝐴𝐴𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡−1+ 𝜀𝜀𝑖𝑖,𝑡𝑡

In contrast to Demirguc-Kunt et al. (2013), the dependent variable Stabilityi,t refers to bank stability for bank i at time t, as the standard deviation of returns, instead of bank’s stock return. Beltratti & Stulz (2012) use the standard deviation of stock return to measure stability. In the spirit of Beltratti & Stulz (2012), this model uses the standard deviation of ROA and ROE. This measure is based on quarterly financials for each company i, in a given year t. Additionally, in the spirit of Beck (2008) the z-score is used to measure bank stability. The z-score indicates the bank’s distance from insolvency, it combines accounting measures of profitability, leverage and volatility. Moreover, it indicates the number of standard deviation that the bank’s return on assets has to drop below its expected value before the bank’s equity position is insufficiently low that the bank is insolvent. z = (ROA+CAR)/SDROA, where CAR is the capital-asset ratio, and is calculated by total equity over total assets. In response to skewness towards large values the logarithm of the z-score is used. The higher the z-score, the more stable a bank is. The main independent variable in this equation is Ki,t-1 , which refers to the lagged capital ratio. Capital is measured in different ratios; Tier 1 capital ratio, Tier 2 capital ratio, and the unweighted ratio. Tier 1 capital ratio is Tier 1 capital over the total risk-weighted assets, Tier 2 capital ratio is the summation of Tier 1 and Tier 2 capital over total risk-weighted assets, and the unweighted ratio is total equity over total assets. The lagged values of the capital ratios and control variables are used to assure that adjustments are incorporated in the measure of bank stability. The sample period is categorized in three sub-periods; pre-crisis, crisis, and post-crisis. Dcrisis is a dummy

variable, taking the value 1, for the observation while the financial crisis was unfolding in 2007-2009. According to Admati et al. (2013) higher capitalized banks suffer fewer distortions and

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13 | P a g e have more stable performance when there are negative shock in asset value. These negative shocks occurred chiefly during the crisis period. The interaction term of capital and the dummy allows the effect of the explanatory variable on bank stability to differ during the crisis period.

CD refers to the control variable cash and due from banks, it is calculated a proportion of total assets, and is used as a measure for the bank’s liquidity. Apart from cash and due from banks, marketable securities are also seen, by financial regulators, as highly rated liquid assets. But they are not equally liquid in different countries. These differences in product market may cause endogeneity, as result of omitted variables. This implies that the explanatory variable is correlated with the error term. To avoid endogeneity, only cash and due from banks is seen as liquidity proxy (Bonner et al., 2015). High cash holding can reduce liquidity risk for banks and could help them survive. Since they have a large amount of liquid assets relatively to their assets, they are better able to deal with unexpected losses. Therefore, it is expected that banks with more cash and due from banks have more stability in returns.

The bank’s deposits variable, DEP, is included and calculated by total deposit over total assets. Berger & Bouwman (2013) state that core deposits are considered to be a stable source of funding. Core deposits include among others; transaction deposits, savings deposits, and small time deposits, these deposits are generally less vulnerable for changes in short-term interest rate. Since depositor are protected through the deposit insurance, there is less risk that demand deposits will cause bank-runs. During the last financial crisis the funding market, which is the interbank lending market, froze and banks did not lend to each other anymore. Banks with a higher deposit ratio were more stable and had fewer change to default (Berger & Bouwman, 2013). Consequently, it is expected that banks that rely more on deposits have more stability in returns.

LLP refers to the control variable of loan loss provision to total assets. Loan loss provision is an expense set aside as an allowance for bad loans. This allowance can be regarded as a reserve in case of loan default. Berger & DeYoung (1997) show that loan loss provision is relatively larger for defaulting banks prior to default. Therefore, they state that loan loss provision can be seen as a significant measure of insolvency. It is expected that banks lower loss loan provision will have more stable returns.

NL is the amount of net loans to total assets. This ratio can be seen as an indicator of credit risk. Credit risk is the risk that arises from a borrower’s failure to repay its loan. The more a bank invests in loan portfolios the higher the exposure for credit risk will be (Demirguc-Kunt et al., 2013). This is why it is expected that there will be a positive relation between the bank’s net loans and stability.

The control variable ASS is measured by the logarithm of total assets. This is a variable control for differences in total assets between banks. In response to skewness to large values of

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14 | P a g e total assets, the logarithm is used. Berger & Bouwman (2013) suggest that bank size is expected to have a positive effect on the probability of survival, because larger banks have higher survival odds than smaller banks. That is, larger banks are better able to diversify their investment and gain profit from economies of scale. Large banks also profit of the too big to fail subsidy, which can be seen as the shift in banks’ cost of fond between small banks and large banks. Since deposits and debts of too big to fail banks are effectively guaranteed by the government, these investments can be seen as safer than with small banks. Therefore, large banks are able to pay lower interest rates to investors than small banks are obliged to pay. Thereby, it is expected that banks with more assets will have more stability in returns. Finally, an interaction term of capital ratio and assets is included in the equation. This term determines whether bank capital has a different influence on banks with a different size. In contrast to Beltratti & Stulz (2012), Berger & Bouwman (2013), and Demirguc-Kunt et al. (2013) this paper distinguishes not on the basis of a size dummy between banks, but on the logarithm of assets. Berger & Bouwman (2013) find that capital helps to increase small banks’ probability of survival at all times, and that it only helps medium and large banks during a crisis. Very large banks may be considered too-big-to-fail. Capital regulation may not improve stability for these bank, as they will be supported by the government when they might become insolvent. So it is expected that a higher capital ratio does not increase stability more for large banks during the crisis and during the non-crisis period it will have a negative influence.

Because the data consist of observations made over multiple years for a specific group of banks, a panel data analysis is done. In order to test whether to use fixed effects or random effects, a Hausman specification test is done on both regressions. The test evaluates the consistency of an estimator in both a fixed effect regression and a random effect regression. As can be seen in Appendix I, the Hausman test shows that this regression is non-random, which implies that the firm fixed effect model is the most appropriate. The model is estimated with ordinary least squares (OLS) estimates. The coefficients to be estimated are α, β, and γ. There might be unobserved variables that are correlated with the independent variable K, that varies over time. These unobserved variables could cause omitted variable bias in a regression model. Including year fixed effects may solve this type of omitted variable bias, when the unobserved variables that vary over time do not vary between company-pairs at a given point in time. In contrast to Demirguc-Kunt et al. (2013), there is no need to include country specific effects, since this sample only uses U.S. bank financials. Robust standard errors are used to deal with possible problems of normality and heteroscedasticity. With the robust option, the estimated coefficients are exactly the same as in ordinary OLS, but the standard errors are larger, because they take into account issues concerning heteroscedasticity and lack of normality. Finally, εi,t is the error term.

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15 | P a g e

3.3 Sample selection

The Compustat data base is used in the sample selection of this research. This data base consists of U.S. banks. All available publicly held banks over the period 2004-2012 are used. The dependent variable in the equation, bank stability, is measured as standard deviation of return on asset and return on equity. Return on asset and return on equity are calculated by the net income of a company i over the total assets or book holders’ equity, respectively. This is done for every company on a quarterly base. The standard deviation is calculated for each company annually, on basis of those four quarters. The data sample contains 6,676 observations, over 1,083 unique companies.

Banks with missing information regarding Tier 1 capital ratio and Tier 2 capital ratio are excluded from the sample, as well as missing information regarding ROA and ROE. Only banks that have at least 3 consecutive years of data are kept in the sample. Additionally, all banks with less than $25 million in total assets are excluded. Banks with 0 deposits, which are pure investment banks, are excluded as well. The National Bank of Greece is excluded from the sample as well, because the LLP is 50 times as high as that of the second bank. All banks with a negative stockholders’ equity value are excluded, because this is often due to the accounting method used to deal with the cumulated losses in previous years. Also banks with negative Tier 1 and Tier 2 ratios are excluded. These adjustments bring the sample back to 4,564 observations, over 616 unique banks.

To control for potential multicollinearity, a variance inflation factors (VIF) test is performed. A VIF test is used to describe how much correlation between variables exists in the regression. This correlation between variables is called multicollinearity, and may be problematic because it can increase the variance of the regression coefficients, making them unstable and hard to interpret. A VIF score between 5 and 10, can be interpreted as highly correlated predictors. As can be seen in Appendix II, a VIF test is done in Stata for all variables within the regression, and none of them exceeds the value of 5. This value suggests that the predictors are moderately correlated with each other, and there is no issue of multicollinearity.

3.4 Descriptive statistics

Table 1 shows the descriptive statistics of the sample data. It shows statistics of stability, measured as standard deviation of ROA and ROE, and the z-score, the different capital ratios, and the control variables, in the full sample, during the crisis period, and during the non-crisis period.As can be seen in Table 1, both the standard deviation of ROA and ROE increases during the crisis period. The volatility of ROE is almost 10 times as volatile than the volatility of ROA during both periods. A larger standard deviation implies there is more volatility in returns. The z-score decreases during the crisis period, which indicates that the number standard deviation

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16 | P a g e of the bank’s return on assets is decreasing, and that there is more chance that the bank will become insolvent. During the crisis period all three capital measures decrease. This may be due to the impact of negative shocks in asset value, which are absorbed by these capital values. The cash and due from banks decreases, as well as the deposits. Loan loss provisions increases, since there was a higher risk of loan default during the crisis. Net loans increases, and the assets drop during the crisis period.

Table 1. Descriptive statistics

Table 1 shows descriptive statistics of bank stability, different capital ratios and control variables obtained from Compustat. The tables shows the average of the full sample, during the crisis period and during the non-crisis period. The table also shows the standard deviation, the minimum and maximum value for the full sample. Bank stability is measured by standard deviation of ROA and ROE, measured for each company in a given year. Z-score is calculated as the logarithm of Z, where Z = (ROA+CAR)/SDROA. Tier 1 ratio is measured as the percentage Tier 1 capital over risk-weighted assets, Tier 2 ratio is measured as the percentage Tier 1 plus Tier 2 capital over risk-weighted assets, and unweighted ratio is measured as the percentage total equity over total assets.

Average Full Sample

Full Crisis Non-Crisis SD Min Max

SDROA (%) 0.2 0.3 0.1 0.4 0.0 6.5 SDROE (%) 1.8 2.8 1.3 3.7 0.0 30.3 Z-score 5.1 4.6 5.4 1.5 -1.5 13.5 Tier 1 (%) 11.9 11.2 12.3 3.8 1.0 54.4 Tier 2 (%) 14.6 14.0 15.0 4.7 2.0 59.0 Unweighted Ratio (%) 9.6 9.5 9.7 3.4 0.3 34.0

Cash and Due from

Banks (%) 4.4 3.9 4.7 4.3 0.0 46.7 Deposits (%) 74.7 73.1 75.7 10.6 18.0 97.1 Loan Loss Provision (%) 0.6 0.8 0.5 0.9 0.0 10.4 Net Loans (%) 66.9 69.4 65.4 13.0 4.5 94.4 Assets ($bn) 53.0 52.7 53.4 267.5 0.06 3771.2 Observations 4564 1693 2871

A clear overview of the distribution over time is shown in the figures below. As can be seen in Exhibit 1 the returns become more volatile during the crisis period, also the average of the returns increases. After the crisis there are still some outliers, but the average returns decrease again. The graph shows clearly that the ROE is more volatility than the ROA. Exhibit 2 shows the distribution of which the Tier 1 capital ratio belongs to the highest 10%. As can be seen both the ROA as the ROE are more stable than in the full sample. During the crisis period, the volatility increase, but less than in the full sample. The same is done for the banks of which the Tier 1 capital ratio belongs to the lowest 10%. The returns are less stable than those of the highest 10%. Also during the crisis period, the return volatility increases more than that of high capitalized banks. Also for the z-score can be seen, that the average of lowest 10% decreases during the crisis, while the highest 10% remains equal. These Exhibits suggest that banks with a higher capital ratio have more stable returns in both the crisis and the non-crisis period.

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Exhibit 2. Stability over time, high Tier 1

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4. Results

Several regressions are done to examine the effect of capital ratios on bank stability. The three different capital ratio; Tier 1, Tier 2, and the unweighted ratio are separately regressed on the standard deviation of ROA and ROE, and the Z-score. The effect of each capital measure on bank stability is regressed in eight different ways, to show the impact of adding control variables, interaction variable of capital ratio and assets, year fixed effects, and firm fixed effects.

4.1 Effect of Tier 1 capital ratio on ROA stability

Table 2 shows the results of the regression of the Tier 1 capital ratio on the stability of ROA. As can be seen a higher Tier 1 capital ratio has an overall stabilizing effect. During the crisis period the results are as expected. The stabilizing effect is even stronger during the crisis, it shows significant results in regression 3, 4, 5 and 7. Adding the control variables does not change the effect of Tier1. This implies that a higher Tier 1 capital ratio ensures for more stability on ROA during the crisis. The effect stay significant when adding time and firm fixed effects. The impact of capital becomes insignificant when the interaction term of Tier 1 and assets is added to the regression. The explanatory effect shifts in these regression to the interaction term. The interaction coefficient of Tier 1 and assets shows that, a higher Tier 1 capital ratio results in more stable ROA when banks are of larger scale. During the crisis there is no significant difference when banks are of larger scale. Not all control variables show the effect as expected. There is a strong positive relation between either loan loss provisions and the logarithm of bank’s assets. This indicates that when a bank has a larger amount for loan loss provisions, or a bank has a larger amount of total assets, it is expected to have less stable ROA. For the loan loss provisions this is as expected, but for the bank’s assets this was expected to be the other way around. Deposits show a negative relation as expected. The other two variables do not show uniform significant results.

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Table 2. Regressions Tier1 on SDROA

Table 2 shows the estimated coefficients of the regressions of Tier 1 capital ratio on bank stability. The crisis period is defined as 2007-2009. Bank stability is measured by standard deviation of ROA, measured for each company in a given year. Tier 1 ratio is measured as Tier 1 capital over risk-weighted assets. CD is measured as cash and due from banks over total assets, DEP is measured as deposits over total assets, LLP is measured as loans loss provisions over total assets, NL is measured as net loans over total assets, and ASS is measured as the logarithm of total assets. Robust standard errors are used.

(1) (2) (3) (4) (5) (6) (7) (8) SDROA SDROA SDROA SDROA SDROA SDROA SDROA SDROA

Tier 1 -0.00911*** -0.00498** -0.00411*** 0.0104 -0.00845*** 0.0170 -0.00706** 0.0177* (-5.50) (-2.40) (-3.32) (1.55) (-2.95) (1.61) (-2.43) (1.69) Tier 1 * crisdum=1 -0.00501 -0.00816** -0.00817* -0.00695** -0.00436 -0.00456** -0.00282 (-1.47) (-2.50) (-1.72) (-2.13) (-0.89) (-2.02) (-0.58) crisdum 0.192*** 0.271*** 0.272*** 0.186*** 0.175*** 0.240*** 0.234*** (4.62) (6.75) (6.40) (4.45) (3.95) (4.94) (4.59) CD 0.00235 0.00241 -0.00181 -0.00135 -0.00186 -0.00150 (1.48) (1.52) (-0.75) (-0.56) (-0.78) (-0.63) DEP -0.00209*** -0.00200*** -0.00591*** -0.00576*** -0.00290* -0.00296* (-3.13) (-2.99) (-3.91) (-3.81) (-1.82) (-1.86) LLP 0.146*** 0.147*** 0.0908*** 0.0913*** 0.0716*** 0.0714*** (20.13) (20.18) (10.57) (10.63) (7.38) (7.36) NL 0.000508 0.000447 -0.000641 -0.000347 -0.00226* -0.00194 (0.96) (0.84) (-0.51) (-0.27) (-1.77) (-1.51) ASS 0.00998*** 0.00803 0.230*** 0.286*** 0.176*** 0.223*** (2.60) (0.74) (8.30) (8.04) (4.74) (5.33) Tier 1 * ASS -0.00165* -0.00349** -0.00342** (-1.81) (-2.50) (-2.45)

Tier 1 * ASS * crisdum=1 -0.00003 -0.00001 -0.00003

(-0.05) (-0.02) (-0.05)

Constant 0.285*** 0.181*** 0.222*** 0.0925 -1.106*** -1.554*** -0.815** -1.178***

(13.85) (6.78) (2.61) (0.82) (-4.13) (-4.83) (-2.37) (-3.15)

Adjusted R2 _0.007 _0.036 _0.152 _0.153 _0.125 _0.127 _0.150 _0.153

Observations 3913 3913 3886 3886 3886 3886 3886 3886

Year fixed effects No No No No No No Yes Yes

Firm fixed effects No No No No Yes Yes Yes Yes

t statistics in parentheses * p<0.10, ** p<0.05, *** p<.01

4.2 Effect of Tier 2 capital ratio on ROA stability

The results of the regressions of the Tier 2 capital ratio on the stability of ROA are shown in Table 3. Tier 2 capital shows the same relation as Tier 1 capital, a higher ratio results in more stable ROA. Tier 2 capital shows also, during the crisis period a stronger stabilizing effect. Adding the control variables do not change this effect, neither do the time and firm fixed effects By adding the interaction term of Tier 2 and assets to the regression, Tier 2 capital decreases is explanatory power. As can be seen, a higher Tier 2 capital ratio results in more stable ROA when banks are of larger scale. During the crisis there is no significant difference when banks are of larger scale. The control variables show the same results as before in Table 2.

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Table 3. Regressions Tier2 on SDROA

Table 3 shows the estimated coefficients of the regressions of Tier 2 capital ratio on bank stability. The crisis period is defined as 2007-2009. ASS is measured as the logarithm of total assets in million dollars. Robust standard errors are used.

Tier 2 -0.00722*** -0.00278 -0.000554 0.0120** -0.00718*** 0.0179* -0.00587** 0.0175* (-5.50) (-1.60) (-0.31) (1.96) (-2.68) (1.85) (-2.16) (1.83) Tier 2 * crisdum=1 -0.00682*** -0.00906*** -0.00800** -0.00546** -0.00466 -0.00494* -0.00388 (-2.61) (-3.63) (-2.15) (-2.12) (-1.23) (-1.94) (-1.04) crisdum 0.233*** 0.306*** 0.309*** 0.208*** 0.204*** 0.270*** 0.271*** (5.87) (8.04) (7.85) (5.26) (4.98) (5.83) (5.69) Tier 2 * ASS -0.00182** -0.00352*** -0.00332** (-2.14) (-2.70) (-2.55) Tier 2 * ASS * crisdum=1 -0.000189 -0.000116 -0.000146 (-0.41) (-0.25) (-0.32) Constant 0.282*** 0.161*** 0.277*** 0.0960 -0.983*** -1.473*** -0.721** -1.108*** (14.07) (5.94) (2.99) (0.77) (-3.57) (-4.47) (-2.05) (-2.89) Adjusted R2 _0.007 _0.038 _0.154 _0.155 _0.125 _0.127 _0.151 _0.153 Observations 3912 3912 3885 3885 3885 3885 3885 3885

Control variables No No Yes Yes Yes Yes Yes Yes

4.3 Effect of Unweighted capital ratio on ROA stability

Table 4 summarizes the results of the unweighted ratio regressed on the ROA stability. In comparison to the Tier 1 and Tier 2 capital ratio, the unweighted ratio does not show uniform stabilizing results. When regression only the unweighted ratio on the standard deviation of ROA, which can be interpreted as the correlation, it shows a positive relation. This implies that on average, an increase in the unweighted ratio results in less stable ROA. Also the effect during the crisis shows positive significant coefficients. The same holds for the interaction term of unweighted ratio and assets. During the crisis period it shows positive significant coefficients, which implies that during the crisis a higher unweighted ratio results in less stable ROA when banks are of larger scale. These results are the opposite as expected and the opposite as shown before with Tier 1 and Tier 2 capital. The control variables show the same results as before in Table 2.

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Table 4. Regressions Unweighted ratio on SDROA

Table 4 shows the estimated coefficients of the regressions of the unweighted ratio on bank stability. The crisis period is defined as 2007-2009. ASS is measured as the logarithm of total assets in million dollars. Robust standard errors are used.

UnweightedRatio 0.00196 -0.00592** -0.00211 0.00116 0.00657* 0.0116 0.00946** 0.00865 (1.08) (-2.40) (-0.88) (0.16) (1.73) (0.80) (2.48) (0.60) UnweightedRatio * crisdum=1 0.0155*** 0.0125*** -0.00216 0.0106*** -0.00571 0.00956*** -0.00579 (4.36) (3.65) (-0.38) (3.08) (-1.00) (2.82) (-1.04) crisdum -0.00950 0.0585* 0.0354 0.0330 0.00663 0.0967** 0.0733* (-0.26) (1.65) (0.98) (0.92) (0.18) (2.23) (1.67) UnweightedRatio * ASS -0.000528 -0.000694 0.000120 (-0.59) (-0.35) (0.06) UnweightedRatio * ASS * crisdum=1 0.00226*** 0.00252*** 0.00236*** (3.17) (3.60) (3.43) Constant 0.158*** 0.176*** 0.128 0.164 -1.618*** -1.668*** -1.565*** -1.525*** (8.56) (7.08) (1.60) (1.55) (-6.12) (-5.08) (-4.65) (-4.02) Adjusted R2 _0.000 _0.036 _0.156 _0.159 _0.128 _0.131 _0.155 _0.158 Observations 3913 3913 3886 3886 3886 3886 3886 3886

Control variables No No Yes Yes Yes Yes Yes Yes

4.4 Effect of capital ratios on ROE stability

The results of the regressions of Tier 1 capital, Tier 2 capital, and the unweighted capital ratio on ROE stability are shown in Appendix III, IV, and V respectively. Appendix III shows the effect of Tier 1 capital ratio and Appendix IV shows the effect of Tier 2. Both tables show results as expected and are in line with the results of capital on ROA. An increase in the Tier 1 and Tier 2 capital ratios show an overall stabilizing effect on ROE, and during the crisis period this effect becomes stronger. The same results hold when adding control variables, and time and firm fixed effects. The interaction term of unweighted ratio and assets shows in both tables that a higher Tier 1 or Tier 2 capital ratio results in more stable ROE when banks are of larger scale. During the crisis there is no significant difference when banks are of larger scale. The results of the unweighted ratio on ROE stability are shown in Appendix V. The results show an overall stabilizing effect of the unweighted ratio. During the crisis period there was no significant difference in the effect. However, by including the interaction term in the regression, the crisis period becomes significant and shows a stabilizing effect. But in contract, the interaction term shows that during the crisis a higher unweighted ratio results in less stable ROE when banks are of larger scale. The control variables show the same results as before.

4.5 Effect of capital ratios on the Z-score

The results of the regressions of Tier 1 capital, Tier 2 capital, and the unweighted capital ratio on the Z-score are shown in Appendix VI, VII, and VIII respectively. The results of Tier 1 and Tier 2 capital are shown in appendix VI and V. The overall results, in the full sample does not

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22 | P a g e show any uniform results. But during the crisis period it does, all regressions show a strong stabilizing effect. Regression without the interaction term of Tier 1 and assets show an overall positive relation, and with the interaction term shows a negative relation. By adding the interaction term the effect of Tier 1 capital will be incorporated in the interaction term, which may affect the coefficient of Tier 1 capital. The interaction term in the full sample shows a positive relation, which indicates a higher Tier 1 or Tier 2 capital ratio results in a more stable Z-score when banks are of larger scale. In comparison to the previous results, shows the interaction term in the crisis period a negative relation. This implies that a higher Tier 1 or Tier 2 capital ratio results in less stability when banks are of larger scale. Appendix XIII shows the effect of the unweighted ratio on the Z-score. The unweighted leverage ratio shows an overall stabilizing effect, but during the crisis period is shows a negative effect. This implies that a higher unweighted ratio, during the crisis, result in less stability, which is the opposite as expected. The control variables show the same results as before.

5. Robustness checks

To test the robustness of the results, several checks are performed. For this check regression 6 of the base regressions is used, which includes both year and firm fixed effects. First, all regressions are run once again with clustered standard errors. The results are shown in Appendix IX. The results are similar as before. Thus, the results are robust when clustering for standard errors.

For the second robustness check the sample is separated in three subsamples; small, medium and large size banks, since the effect of capital may differ by bank size (Berger & Bouwman, 2013). Small banks are defined when they consist of total assets up to $1 billion, medium banks exceeding $1 billion up to $3 billion, and large banks exceeding $3 billion. Again, only regression 6 is used, which includes both year and firm fixed effects. Table 5 shows the results of the three different capital measures on the stability of ROA for each of the three subsamples. As can be seen in the table below, a higher Tier 1 capital ratio has an overall stabilizing effect on ROA for small and large size banks. During the crisis period there is no significant difference. The results show no significant result for medium size banks. A higher Tier 1 capital ratio has only a stabilizing effect on ROA for large size banks. Again, the crisis period shows no significant difference. A higher unweighted ratio shows a significant positive relation for medium and large size banks, which is the opposite as expected. This confirms the previous results, that the unweighted ratio is an inappropriate measure to ensure return stability. Appendix X shows the same regressions but uses the standard deviation of ROE as stability measure. These results are in line with the results on ROA stability. Only Tier 1 and Tier

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23 | P a g e 2 capital for small and large size banks show significant stabilizing effects. The unweighted ratio does not show any significant results for any subsample. Appendix XI uses the z-score as stability measure. Tier 1 capital only shows a stabilizing result for small size banks. During the crisis period this effect is even stronger. Tier 2 show again only a stabilizing effect for small and large size banks, for small banks the effect is stronger during the crisis period, for large banks it is only significant during the crisis period. In comparison to previous results, the unweighted ratio shows a significant stabilizing result for small and large size banks. For small banks the effect gets stronger during the crisis period, for large banks it is again only significant during the crisis period. These results suggest that the results in the base regressions are not robust for all banks. When controlling for bank size, capital ratios show that the stabilizing effect does not hold any longer for medium size banks, but only for small and large banks.

For the third robustness check the sample period is adjusted to only the pre-crisis period and crisis-period, excluding the post-crisis period. This excludes the spillover effect of the crisis in the years 2010-2012. Again, only regression 6 is used, which includes both year and firm fixed effects. Table 6 shows the results of this check with standard deviation of ROA and stability measure. In comparison to Table 5, Tier 1 and Tier 2 capital show only significant stabilizing effect on ROA stability for small size banks. The results show no significant difference in the crisis period. The unweighted show a positive relation for medium size banks, which confirms again that the unweighted ratio is inappropriate. For both small and large size banks the effect is not significant. Appendix XII shows the results on ROE stability. This table shows the same results as before. Tier 1 and Tier 2 capital only show a significant stabilizing effect of ROE stability for small size banks. Again, the results show no difference in the crisis period. The unweighted ratio confirms the previous results as well, and shows a positive relation for small and medium size banks. Appendix XIII show the results on the z-score. This table shows different results as before. Tier 1 shows an overall stabilizing effect for small size banks, but for medium and large size banks it shows a destabilizing effect. Additionally, during the crisis Tier 1 shows a stronger effect for small banks, and also show a stabilizing effect for medium and large size banks. Tier 2 shows the same results as Tier 1. The unweighted ratio shows a stabilizing effect for small size banks. During the crisis period this effect becomes stronger. These results show again, that the results in the base regressions are not robust for all banks. When controlling for bank size and the spillover effect after the crisis, capital ratios show that the stabilizing effect does not hold any longer for medium and large size banks, but only for small banks. The z-score shows that Tier 1 and Tier 2 has a stabilizing effect on small banks at all time, but for medium and large banks only during the crisis period.

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Table 5. Robustness check 2: Small, Medium, and Large Banks

Table 5 shows the estimated coefficients of the regressions of Tier 1 capital ratio, Tier 2 capital ratio, and UnweightedRatio on ROA stability. The crisis period is defined as 2007-2009. Small banks are defined when they consist of total assets up to $1 billion, medium banks exceeding $1 billion up to $3 billion, and large banks exceeding $3 billion. Robust standard errors are used.

Small Banks Medium Banks Large Banks

(1) (2) (3) (4) (5) (6) (7) (8) (9)

SDROA SDROA SDROA SDROA SDROA SDROA SDROA SDROA SDROA

Tier 1 -0.00736* 0.00180 -0.0153** (-1.76) (0.24) (-2.57) Tier 1 * crisdum=1 0.00232 -0.00469 0.00197 (0.52) (-0.57) (0.26) Tier 2 -0.00551 0.000144 -0.0104* (-1.48) (0.02) (-1.78) Tier 2 * crisdum=1 -0.00254 -0.00109 -0.00601 (-0.75) (-0.20) (-0.84) UnweightedRatio 0.00633 0.0297*** 0.00350 (1.15) (3.27) (0.43) UnweightedRatio * crisdum=1 -0.00160 0.0197*** 0.0216*** (-0.33) (2.63) (3.25) Constant -0.850* -0.701 -1.464*** -3.588*** -3.576*** -4.502*** 0.656 0.676 -0.200 (-1.70) (-1.34) (-2.95) (-4.54) (-4.44) (-5.88) (0.89) (0.90) (-0.28) Adjusted R2 _0.130 _0.131 _0.115 _0.157 _0.156 _0.143 _0.136 _0.137 _0.126 Observations 1527 1527 1527 1145 1145 1145 1214 1213 1214

Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes

Year fixed effects Yes Yes Yes Yes Yes Yes Yes Yes Yes

Firm Fixed effects Yes Yes Yes Yes Yes Yes Yes Yes Yes

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Table 6. Robustness check 3: Small, Medium, and Large Banks, pre-crisis and crisis period only (2004-2009)

Table 6 shows the estimated coefficients of the regressions of Tier 1 capital ratio, Tier 2 capital ratio, and UnweightedRatio on ROA stability. The crisis period is defined as 2007-2009. Small banks are defined when they consist of total assets up to $1 billion, medium banks exceeding $1 billion up to $3 billion, and large banks exceeding $3 billion. Robust standard errors are used.

Small Banks Medium Banks Large Banks

(1) (2) (3) (4) (5) (6) (7) (8) (9)

SDROA SDROA SDROA SDROA SDROA SDROA SDROA SDROA SDROA

Tier 1 -0.0184** 0.0132 0.00623 (-2.48) (0.71) (0.63) Tier 1 * crisdum=1 0.00534 -0.00357 0.000633 (0.71) (-0.20) (0.06) Tier 2 -0.0141** 0.0120 0.00403 (-2.32) (0.65) (0.41) Tier 2 * crisdum=1 -0.00611 -0.00264 -0.00851 (-1.04) (-0.15) (-0.78) UnweightedRatio -0.00223 -0.00830 0.0174 (-0.23) (-0.42) (1.12) UnweightedRatio * crisdum=1 -0.00144 0.0856*** 0.0191 (-0.17) (5.16) (1.63) Constant 0.136 0.466 -0.584 -5.467*** -5.482*** -4.466*** -1.862 -1.600 -1.962 (0.17) (0.55) (-0.74) (-3.42) (-3.36) (-3.03) (-1.37) (-1.16) (-1.49) Adjusted R2 _0.151 _0.153 _0.138 _0.180 _0.180 _0.152 _0.144 _0.142 _0.136 Observations 1527 1527 1527 1145 1145 1145 1214 1213 1214

Control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes

Year fixed effects Yes Yes Yes Yes Yes Yes Yes Yes Yes

Firm Fixed effects Yes Yes Yes Yes Yes Yes Yes Yes Yes

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6. Discussion

There is currently a discussion going on about the policy implication of capital regulation. Specifically; which regulatory measure ensures bank stability the best; the risk-based capital ratio or a uniform capital ratio, like the unweighted leverage ratio. Kim & Santomero (1988) suggest that the use of a uniform capital ratio in regulation is an ineffective resolution to lower the risk of default. Their reasoning is that the use of a uniform capital ratio ignores the individual banks’ different preference structures and allows banks to avoid the regulation by the usage of leverage or business risk. But in contrast, Demirguc-Kunt et al. (2013) suggest that the effect of capital on stock returns during the crisis is more sensitive to the leverage ratio than the risk-based capital ratio. This may be because the risk-based capital ratios under Basel rules are subject to manipulation or in any case not reflective of true risk in the case of large banks. In 2013 a Dutch committee is assigned to improve the stability and compliance of the Dutch banking system. In their report “Naar een dienstbaar en stabile bankwezen (2013)” they present several recommendations that may improve the banking system. One of their recommendations is to increase the leverage ratio, instead of the risk-based capital ratio. They suggest that the risk-based ratio is based on internal models, which may vary widely and may be misleading to the regulators. Additionally, they argue that regulators have managed to get the risk weights of specific assets wrong, for example the risk-weighted of most government bonds are 0%, while investing in some of those countries may not be considered as risk-free.

Last month the Financial CHOICE Act is announced in the United States, which should fundamentally reform the Dodd-Frank act. Financial institutions would have to surpass critical thresholds, including a 10% leverage ratio. Increasing the leverage ratio, instead of the risk-based ratio, would relieve financial institutions from regulations that create more distortions than benefit in exchange for meeting higher capital requirements. They suggest that risk-weighted capital is simply not as effective. First, it is far too complex. Second, it confers a competitive advantage on those large financial institutions that have the resources to navigate its complexity. Third, regulators have managed to get the risk weights of assets wrong, for example, treating mortgage-backed securities and Greek sovereign debt as almost risk-free. (Financial CHOICE Act, 2016)

The findings of this research are in line with the findings of Kim & Santomero (1988), and suggest that risk-weighted capital ratios are a more appropriate regulatory measure to ensure bank stability. As is shown in the previous two sections, the unweighted leverage ratio has contradictive, and sometimes even volatility increasing effects on bank stability. In Contrast, Tier 1 and Tier 2 capital ratios show an overall stabilizing effect on bank returns.

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7. Conclusion

In response to the latest crisis the Basel Committee on banking supervision introduced the Basel III framework. Basel III aims to improve the stability in the banking sector through, among other, more stringent capital measures. However, existing literature on capital standards and bank stability show ambiguous results. This study analyzes the effect of bank capital on bank stability during the global financial crisis of 2007. Specifically, the relation between bank stability, measured as the standard deviation of ROA and ROE and the z-score, and capital, measured as Tier 1 capital ratio, Tier 2 capital ratio, and the unweighted ratio. A data sample of 4,564 observations, over 616 unique US banks for the period 2004-2012 is used. The crisis period is indicated from 2007-2009. The results are as follows. Banks with a higher Tier 1 and Tier 2 capital ratio have more stable ROA and ROE and a higher z-score, during the crisis period. This indicates that higher capitalized banks are better able to deal with negative shock in asset value, which is in line with the findings of Beltratti & Stulz (2012), and the set hypothesis. Additionally, higher capital ratios also have a stabilizing effect on returns during the non-crisis period. The unweighted ratio shows no uniform results. This suggests that the unweighted ratio is an inappropriate capital measure to limit volatility in returns. This is in line to the findings of Kim & Santomero (1988), but is contrary to Demirguc-Kunt et al. (2013). Demirguc-Kunt et al (2013) suggest that that during the crisis stock returns were more sensitive to the leverage ratio than to the risk-based capital ratio. This paper shows that risk-based capital is more effective to increase bank stability, because it includes the individual banks’ different preference structures.

Including the interaction term of capital ratio and assets in the regression shows whether bank capital has a different influence on banks with a variable size. The results show that, on average, an increase in Tier 1 and Tier 2 capital ratio results in more stability when banks are of larger scale. During the crisis period, there is no significant different effect when banks are of larger scale. Again, the results of the unweighted ratio show no significant coefficients, which endorse the fact that the unweighted ratio is an inappropriate capital measure.

Several robustness checks are done. There are different results when the sample is separated between small, medium, and large size banks. The results show that Tier 1 and Tier 2 capital only have a stabilizing effect on small and large size banks. Medium size banks do not show any significant effects. The results are remarkable when banks are separated by size, and the sample is reduced to only the pre-crisis and crisis period, which excludes the spillover period after the crisis. This shows that Tier 1 and Tier 2 capital only has a stabilizing effect on the standard deviation of ROA and ROE for small size banks, and has no significant effect on

Capital ratios and bank stability