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THE IMPACT OF DERIVATIVES HOLDINGS ON

THE FINANCIAL STABILITY OF U.S. BANKS

AND ITS CONTRIBUTION TO SYSTEMIC RISK.

by

Arjen Boeve

Student number: 3259188

Email: a.a.boeve.1@student.rug.nl

MSc International Economics & Business 2017 – 2018 University of Groningen

Faculty of Economics and Business PO Box 800

9700 AV Groningen The Netherlands

Supervisor: dr. P.A. IJtsma Co-assessor: dr. A.C. Steiner

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Abstract

Growth in the derivatives market has been considerable in recent decades. This study analyses the influence of derivatives holdings on the financial stability of U.S. banks and their contribution to systemic risk. Banks’ individual Z-scores are used as a proxy for individual risk. The empirical analysis is based on panel data from 50 U.S banks for the period 2000–2017. The study uses a fixed-effects model and conducts a dynamic GMM estimator as a robustness check. The results imply that possessing credit derivatives increases the financial stability of banks, whereas their holdings of exchange-rate derivatives decrease financial stability. However, the robustness checks do not confirm all these findings. The system-wide analysis does not provide robust evidence for the impact of financial derivatives on systemic risk for the whole sample frame. Nevertheless, the results of the analysis of the interest-rate derivatives suggests that banks used interest-rate derivatives more for speculative purposes before the global financial crisis and more for hedging purposes following the crisis. Regulation should be carefully designed because it could hinder derivative activities that could in fact increase financial stability at the individual and/or system level.

Keywords: financial stability, derivative holdings, systemic risk, U.S. banks.

JEL Classifications: C33, G01, G21, G23

Acknowledgements

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Table of Contents 1. Introduction ... 4 2. Literature Review ... 6 2.1 Theoretical ... 6 2.2 Empirical ... 8 3. Research Design ... 11 3.1 Methodology ... 12 3.2 Empirical model ... 17 3.3 Control variables ... 19 4. Data ... 20

4.1 Sources and sample ... 20

4.2 Summary statistics ... 22

4.3 Panel data assumptions ... 25

5. Empirical Results ... 28

5.1 Main results ... 28

5.2 Further analysis and robustness tests ... 32

6. Conclusion ... 36

7. References ... 39

Appendix A - Data appendix ... 44

Appendix B – Panel data tests ... 46

Appendix C – Data (trends) ... 49

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4

1. INTRODUCTION

The stability of banks is vital for an economy. Despite this, banking crises have been a common phenomenon throughout history. Reinhart and Rogoff (2009) found over 250 banking crises in the last decades, with their frequency increasing more recently. Famous examples are the U.S. savings and loans debacle of the 1980s, the 1997 Asian crisis, and the 1998 Russian crisis. The recent financial crisis of 2007/8 has shown that banking crises are often found at the centre of a financial crisis (Laeven, 2011). The fall of large banks, among them Lehman Brothers, Bear Stearns, and Northern Rock have, once more, illustrated the importance of a stable financial system. Indeed, banking crises hurt economic growth (Dell’Ariccia et al., 2008). Before the crisis, the consensus in the literature was to examine the risk management of individual financial institutions or banks. When a bank had enough liquidity, was solvent, and met the standards, the entire system would be safe. However, the recent financial crisis has shown that the stability of individual institutions alone is not sufficient to ensure the stability of the financial system as a whole. Hence, systemic risk, which is the possibility that an event at the company level could trigger severe instability in the entire economy, is of particular concern. The crisis shifted the focus from risk management of individual financial institutions to a more system-wide (systemic risk) approach. Nevertheless, the stability of individual banks remains important for the stability of the economy (Drakos & Kouretas, 2015).

These new insights have drawn the attention of several researchers who aim to rediscover the relationships of the variables that are important for financial stability in order to find the causes of instability. The market for derivatives has especially been under the spotlight since the last economic crisis. Historically, derivative products were seen as the primary cause of success in financial risk management and were believed to have contributed to the resilience of the financial system (IMF, 2003). However, since the recent global crisis, critics of derivative products are increasingly vocal in the debate. The financial instruments that were once designed to reduce risk may now be a drag on economic growth as they alter the risk-taking behaviour of banks (Lerner & Tufano, 2011). However, there is no unambiguous answer to the question of the relationship between financial derivatives and their influence on financial stability, which is highly surprising given the growing importance of derivative holdings. To illustrate, in 1995, the total value of derivatives in U.S. banks was less than $18 trillion (Li & Marinč, 2014). Today, the Citigroup bank alone possesses more than $50 trillion in total derivatives (FDIC, 2018).

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5 The U.S. is an interesting market to investigate due to its tremendous growth in derivatives and the wide availability of data. It is, to my knowledge, the only country with such a rich database on the derivatives holdings of banks and their underlying classes.

A few studies have attempted to uncover the impact of derivatives holdings; however, they are incomplete. For example, Ghosh (2017) conducted an analysis of commercial U.S. banks and found that interest-rate and exchange-rate derivatives reduce banks’ insolvency risks. However, his study failed to investigate the role of systemic risk and, therefore, misses an essential part of risk in the financial sector. There are some papers, such as Mayordomo et al. (2014), that focus on systemic risk. The limitation of these papers is that they do not take individual bank stability into account. Individual banks remain important because a country may have a relatively robust financial system even though individual banks take numerous risks. The relationship between banks’ derivatives holdings and financial stability is still quite puzzling.

The contribution of this thesis is fourfold. First, this study offers an addition to studies of Keffala (2015) and Chaudhry et al. (2000) by focusing not only on a small component of total derivatives holdings, such as futures, options, or swaps, which can serve different purposes. Rather, by investigating the classes of derivatives (e.g. credit, exchange-rate, and interest-rate derivatives, etc.) a more complete view is provided. To achieve this, the study incorporates new insights on measurements of financial stability and uses the Z-score as a proxy for the solvency of individual banks; this is used in most (recent) bank-level analyses (e.g. Laeven & Levine, 2009; IJtsma et al., 2017). Second, this is the first study to investigate the effect of banks’ derivatives holdings, both at the individual bank level and at a system-wide level. According to López-Espinosa et al. (2012), there are substantial differences between micro-prudential measures, such as the Z-score, and the macro-prudential approach, the systemic risk. These do not perfectly correlate, making this study a valuable contribution to the existing literature. This study measures systemic risk using the well-known SRISK (Brownlees & Engle, 2016) and LRMES for robustness purposes (Acharya et al., 2012). Third, I want to include the influence of the recent financial crisis. Previous papers on this subject, such as Mayordomo et al. (2014), do not assess whether the relation between the derivatives holdings of banks and the systemic risk has changed following the crisis. Fourth, by making use of a study of U.S. banks, several robustness checks, and more recent data than existing studies on the topic, this research strives to complement the existing knowledge.

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2. LITERATURE REVIEW 2.1 Theoretical

Numerous studies have attempted to define financial stability, the central concept of this research. However, there is as yet no consensus on the definition of financial (in)stability as such. Allen and Wood (2006) identify a number of features that a good definition of financial (in)stability should incorporate. They conclude that financial stability should be, among other things, related to welfare, an observable state of affairs, influenced by public authorities, and not so demanding that virtually any change is evidence for instability. Financial stability is a broad concept that could include several characteristics of a country, for example, the real economy, the financial system, and interactions between countries. Therefore, most definitions refer to the state of the financial system as a whole.

This makes it even more striking that most research only investigates the effect on individual banks and does not take system-wide effects into account. Moreover, individual bank stability and systematic risk are fundamentally different. For instance, Beale et al. (2014) provide an example of a fragile financial system with stable banks. When all banks in a country have the same portfolio, implying that they diversify similarly and have highly correlated risks, then the probability increases that if one bank fails, the others will follow, hence increasing the probability of multiple defaults. Therefore, I use a very broad definition of financial stability as stated by the European Central Bank (2005), namely: ‘financial stability is maintaining the smooth functioning of the financial system and its ability to facilitate and support the efficient functioning and performance of the economy’ (p. 103). It is important to look at both the individual banks and system-wide stability because a stable financial system needs healthy banks and those banks cannot operate in an unstable system. This study focuses on both levels of stability, on the individual banks (default risk) and on the systemic risk (system-wide stability) of the country.

Before elaborating on the effects of banks’ derivatives holdings on financial stability, the concept of derivatives holdings is defined: derivatives are ‘financial contracts between two parties, whose value is contingent on the future price of an asset such as a share, a currency, a commodity, or an index’ (Capelle-Blancard, 2010, p. 68).

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7 funding, and make the lending policies of banks less sensitive to macroeconomic shocks. Hence, a bank would be able to focus on its core activity: monitoring its borrowers. Several later studies have identified the positive effects of banks using derivatives. Chance and Brooks (2009) and Broccardo et al. (2014) show that by using derivatives as protective strategies, banks can preserve and transfer the risk associated with their investments portfolios against market volatility by limiting their losses. Banks and other institutions have recognised the importance of derivatives for dealing with the volatility of interest rates and currencies by using futures swaps and other derivatives to reduce their risk. Derivatives make the market more complete and enrich access to commodities, the transactions costs of which would otherwise be too high. Furthermore, derivatives offer information about the future value of financial assets and provide a payoff that otherwise could not have been obtained from the existing assets, so that risk is more easily shared.1

On the other hand, several studies focus on the dangers of derivatives holdings. Capelle-Blancard (2010) concludes that derivatives provide banks with incentives to take excessive risks, which could hinder the optimal allocation of risks. Furthermore, derivatives create new markets for banks, which introduces a new form of risk that is difficult to assess. Blundell-Wignall and Atkinson (2011) find several other purposes for trading in derivatives other than as positive risk-hedging instruments. First, derivatives could be used for speculative purposes. This can be highly profitable for a bank, but high-risk investments are made and churned. This can lead to large losses as well as gains. Second, there is also a group of derivatives that is used for regulatory arbitrage. The rules of Basel III on capital adequacy ratios are primarily aimed at banks’ lending activities and the trading of equity and debt instruments, while derivative markets are excluded from these requirements (Ghosh, 2017). Finally, derivatives could be used to shift risk to places with lower capital charges. Banks act as derivative dealers without thinking about the consequences of their positions (Minton et al., 2009).

As already becomes clear, there are many different channels through which banks’ derivatives holdings may affect financial stability. As noted by Instefjord (2005), there may be a dual effect of credit derivatives on risk. For instance, when a bank uses derivatives instruments such as credit derivatives, this typically generates two outcomes: on the one hand, it enhances risk-sharing through the distribution of credit risk, as used in the hedging argument; however, on the other hand, it makes further acquisition of risk more attractive. To conclude, although the exact shape of the relationship between bank’s derivatives and financial stability remains unclear, the existing literature does agree that a relationship between several categories of

1 See Capelle-Blancard (2010) for an illustration of this argument. This study provides evidence of easy risk sharing

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8 bank’s derivatives and financial stability can be expected. To establish testable hypotheses, I now turn to empirical research on the topic.

2.2 Empirical

It is valuable to compare the effects of derivatives holdings on both stability of individual banks and on its relation to systemic risk contribution, because, as indicated above, these do not perfectly correlate (López-Espinosa et al., 2012). Moreover, the theoretical study reveals several reasons for banks holding derivatives. Therefore, it is important to study the effects of different classes of derivatives on the financial stability of individual banks and on system-wide stability, because the overall effect may not reveal the whole picture of the different end-user purposes of the derivative holder. The potential impact of the different classes of derivatives holdings on both individual bank stability and system-wide stability has not yet been investigated in one study. First, I focus on the effects on individual bank risk.

2.2.1 Individual banks

The limited empirical literature on bank-specific risks lacks consensus. Li and Yu (2010) investigated the effects of derivatives activity on the 25 largest bank holding companies in the U.S. from April 2005 to September 2008. They found that derivatives holdings increase bank holdings’ overall risk level, as measured by the volatility of the asset values. Banks that are heavily and widely involved in the derivative markets hold derivative positions with the intention of hedging underlying risk, while banks that are comparably less involved in derivative markets take more speculative positions in derivatives contracts. Their study does not specify the type of derivatives. They only investigate the effects of the total notional value of derivatives. The positive effects of one class of derivatives can undo the negative effects of another class if one focuses only on the aggregate values of derivatives. Therefore, they could be missing important information.

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9 measure the ultimate goal, because individual derivatives (e.g. swaps) can fulfil different functions (e.g. interest, exchange and commodity exchange) and their value is based on the prices of the underlying classes (Capelle-Blancard, 2010).

Most studies that include classes of derivatives focus only on one class, principally credit derivatives, due to the relatively great availability of data on these and the fact that banks are major participants in these markets. For example, Rodríguez et al. (2015) found that the use of credit derivatives has a significant positive impact on the Z-scores of European banks. Those banks experienced an improvement in financial stability when they used credit derivatives in their hedging portfolios. Ghosh (2017) investigated all the classes of derivatives. That study used data from 5,000 U.S. commercial banks and found that aggregate derivatives and both interest-rate and exchange-rate derivatives reduce banks’ risks, as measured by the Z-score. The findings hold for large and profitable banks and for banks with the largest share of derivative assets. However, in the post-crisis period (2009–2016), such significance wanes. The results of Ghosh (2017) imply that banks have effectively used several categories of derivatives to reduce their insolvency risks by taking off-setting positions arising from their on-balance activities.

To summarize, there is neither consistent empirical evidence nor a theoretical consensus that leads to an answer to the question of what the impact of banks’ derivatives holdings is on the financial stability of individual banks. Nonetheless, studies do agree that there is an effect. Moreover, the studies that focus on one of several classes of banks’ derivatives holdings find a positive impact on the financial stability of individual banks. The first part of this study focuses on the effects of different classes on derivatives in U.S. banks, which is mostly related to Ghosh (2017). Therefore, the hypothesis regarding individual stability is:

Hypothesis 1: Banks’ derivatives holdings increase the financial stability of individual banks. This holds for all the classes of derivatives.

2.2.2 System-wide effects

The global financial crisis revealed severe weaknesses in the financial system, which opened the way for a more systemic point of view. It does not have to hold that the derivatives holdings of a bank has similar effects on the individual stability of banks as it has on systemic contribution. Wagner (2010) shows that diversification reduces the likelihood of the failure of individual banks, but increases the chance of systematic crises. Financial stability does depend on the correlation of bank returns. A number of studies have attempted to establish a link between banks’ derivatives holdings and systemic risk; however, their results are inconclusive.

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10 primarily to diversify and thus to reduce their risk exposure. However, the evidence is limited, with the strongest results for large borrowers, and focuses only on a part of the derivatives (credit) and on systemic risk (interest-rate risk).

There are also studies that have found an inconclusive effect of aggregate derivatives holdings on systemic risk (Cyree et al., 2012; Mayordomo et al., 2014). They found that the proportion of non-performing loans as a percentage of total assets and the leverage ratio of a bank had a stronger impact on systemic risk than do derivatives holdings. According to Cyree et al. (2012), the reason for the inconclusive relationship might be, due to the fact that banks are expected to trade off the marginal benefits of their leverage on the derivatives operations and the cost of losing their charter due to the increased probability of bankruptcy. Hence, banks regulate volumes in a responsible manner. However, Blundell-Wignall and Atkinson (2011) elaborate on the fact that derivatives grow at an exponential rate compared to the primary securities on which they are based. Therefore, it is difficult to believe that derivatives are mostly used for hedging purposes. Instead, it is more likely that they are based on less socially useful activities, such as speculation, which increases (systemic) risk.

In the empirical literature on banks’ derivatives holdings and systemic risk, several factors at the macroeconomic level have been discussed that could have a negative influence on systemic risk. According to Giglio et al. (2016), historical systemic-risk events affect the real economy, and lead to global recessions and employment losses. Mayordomo et al. (2014) is the first, and only, study that conducted research on all five different classes of derivatives and their effect on systemic risk. They conclude that certain specific types of derivatives, such as exchange-rate and credit derivatives, contribute to systemic risk, whereas holdings of interest-rate derivatives decrease it. This effect may be due to the fact that banks’ positions for credit and exchange-rate derivatives are held for trading activities, rather than for hedging loans. Moreover, Fan et al. (2009) suggest that when a bank uses exchange-rate derivatives to hedge against foreign-exchange risk, they could engage in trading activities at the same time. Hence, using exchange-rate derivatives for hedging purposes is offset by an increase in trading activities. On the contrary, Christoffersen et al. (2009) showed that there is a negative relation between the use of interest-rate derivatives and interest-rate movements. This indicates that interest-rate derivatives have been used more frequently to hedge interest-rate risk rather than for speculative purposes (Minton et al., 2009; Mayordomo et al., 2014). However, this finding is only supported by researchers who study systemic risk. There is no evidence for this at the level of the individual bank.

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11 study does not contain one overall measure of systemic risk. The authors divided systemic risk into interest-rate risk, exchange-rate risk, and credit risk. They found that derivatives held for both trading and hedging purposes are both significantly related to an increase in systemic risk. In addition, Nijskens and Wagner (2011) conclude that while banks may have shed their individual credit risk by means of credit derivatives, banks actually pose a greater systemic risk. However, they focus only on credit default swaps, which are merely one part of credit derivatives. An increase in bank risk is not due to banks overcompensating for the risk they have shared by increasing their lending or leveraging up their capital structure, but is due to the fact that credit risk-transfer activities expose banks to greater systemic risk. More importantly, the study of Minton et al. (2009) shows that even when banks have been in a situation where they simultaneously buy and sell derivatives to the same degree (a situation referred to as a matched book), these ‘neutral’ positions may create systemic risk because there is still counterparty risk. For instance, a bank could be a counterparty on different derivatives with many other financial institutions, so that the collapse of a large bank creates system-wide instability. Hence, a bank that does not endanger its individual stability, can contribute to the systematic risk for the system as a whole.

Based on the results of the abovementioned studies, one can say that, in most cases, a negative relation is found between banks’ derivatives holdings and several classes derivatives as regards system-wide stability due to an enormous increase in banks’ derivatives holdings and the evidence of a lack of the hedging versus trading purposes. The only exception are interest-rate derivatives, which are often found to have a positive effect on systemic risk due to their use for hedging rather than for trading purposes. Therefore, the hypothesis for system-wide stability is:

Hypothesis 2: Banks’ holdings of credit, exchange-rate, and commodity and equity derivatives increase systemic risk, whereas interest-rate derivatives reduce it.

3. RESEARCH DESIGN

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12 To analyse the effects of bank’s derivatives holdings on the contribution to financial (in)stability of the banking sector in the U.S., this study investigates the effects of several classes of derivatives, following (Ghosh, 2017). While forwards, futures, options, and swaps can be viewed as the mechanics of derivation, the value of these contracts is based on the prices of the underlying assets. These underlying assets derive their value from the performance of underlying classes (Capelle-Blancard, 2010). Therefore, it is important to study the classes of derivatives and not only to focus on one sort of derivative. For example, if we only count the notional value of swaps, relevant information may be overlooked as swaps can fulfil different functions. An interest-rate swap involves an exchange between a fixed and a floating rate, while a foreign-exchange swap is the simultaneous purchase and sale of currency with different value dates. Therefore, it is more useful to study the ultimate goal within the classes than to focus on only one instrument that can be used for different purposes (Whaley, 2006; Capelle-Blancard, 2010).

The literature describes five underlying classes, with equity and commodity derivatives often being categorised in the same class. The other classes are credit derivatives (financial assets whose price is driven by the credit risk of economic agents), interest-rates derivatives (financial instruments that increase and decrease in value based on movements in interest rates) and exchange-rate derivatives (the value of which depends on the foreign exchange rate(s) of two (or more) currencies). Each class contains different types of derivatives holdings, such as different kinds of swaps (interest and exchange rate), futures and forwards, written and purchased option contracts, and spot foreign contracts. Hence, all the different functions of banks’ derivatives holdings at both the bank level and the country level are measured in order to obtain a complete view of their influence on financial stability.

3.1 Methodology

3.1.1 Individual bank risk

As mentioned above, the bank-level analysis takes the Z-score as a proxy for the financial stability of individual banks. The Z-score is a highly skewed measure that violates the assumption of normally distributed data. Therefore, following Lepetit and Strobel (2013) and

Keffala, (2015),2 this study uses the natural logarithm of the Z-score, which is approximately

normally distributed. The Z-score is an accounting measure of bank stability where insolvency

risk of a bank is based on the size of a bank’s buffer and is used extensively in the literature.3

2 As shown by Lepetit and Strobel (2015), the logarithm of the Z-score is related to an upper bound of the

probability of insolvency, for all bank’s distribution of returns. Some studies transform the Z-score to avoid observations with negative Z-scores. However, the sample in this study does not contain negative values. Hence, a transformation is not necessary.

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13 The Z-score is a measure of bank risk-taking which equals the return on assets plus the capital asset ratio divided by the standard deviation of asset returns. It combines information about profitability, capital buffers and return volatility. Fu et al. (2014) conclude that the Z-score is related to the probability of a bank’s insolvency. The Z-score measures the distance from insolvency, i.e. where losses surmount equity. The Z-score is the number of standard deviations that a bank has to drop below its expected value before equity is depleted and the bank is insolvent. Moreover, Fu et al. (2014) argue that a higher Z-score implies lower probability of default, hence, higher bank stability. IJtsma et al. (2017) define the Z-score as follows:

𝑍 − 𝑠𝑐𝑜𝑟𝑒 𝑖,𝑡𝐵 = 𝐸(𝑟𝑖𝑡)+ 𝑘(𝑖𝑡)

𝜎(𝑟𝑖𝑡) , (1)

where 𝐸(𝑟𝑖𝑡) is equal to 𝐸 (𝜋𝑖𝑡

𝑎𝑖𝑡), which is the bank’s expected return on assets at time t. This is

calculated bythe expected net income in the following period divided by the total assets. The

next part 𝑘(𝑖𝑡) is equal to (𝑒𝑖𝑡

𝑎𝑖𝑡), which stands for the equity ratio at time t. This can be calculated

by dividing total equity by total assets. Lastly, 𝜎(𝑟𝑖𝑡) is the standard deviation of the return on

assets. Lepetit and Stober (2013) suggest that in order to calculate standard deviations of returns, it is better to use the entire sample period because this presents the optimal estimates of the return volatility. This study follows this reasoning.

The Z-score does not require large amounts of data and has a straightforward interpretation. Because of those reasons, the Z-score is still used in most recent literature on financial stability and in almost all literature on the financial stability of individual banks. Therefore, this will be the starting point of this research as well. However, the Z-score measurement contains some important drawbacks. First, the Z-score does not take the size of banks into account. A bank with a large assets value is equally important as a very small bank. Moreover, the Z-score is a backward-looking risk measure since it uses historical accounting data. Past returns may not always provide an accurate prediction of the expected returns, especially not in uncertain economic times (Agarwal & Taffler, 2007). Nonetheless, the forward-looking measures fail on the bank level. For example, the distance-to-default and other forward-looking individual measures such as the value-at-risk require more data, which would decrease the sample size significantly and would restrain the ability to perform a quantitative analysis. Even more, Nagel and Purnanandam (2015) conclude that the distance-to-default alternative is not appropriate because it assumes that the market value of assets is normally distributed which does not hold for banks.4 However, the Z-score also make assumptions of normally distributed data, but

4 Nagel and Purnanandam (2015) argue that banks assets are risky debt claims which implies a nonlinear asset

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14 focuses on the returns. Those returns might in reality not be normally distributed and therefore not accurately describe the tails of the return distribution which can be seen as the most important part for estimating insolvency risk. Despite these arguments, Agarwal and Traffler (2007) conclude that Z-score models continue to have significant value for credit risk and financial health. Hence, it can be seen as the best alternative for measuring individual stability in this research.

In order to control for robustness, this study uses the risk-adjusted return on equity (ROE) as an alternative measure of the Z-score, following Ghosh (2017). The risk-adjusted return on equity is defined as:

Risk − adjusted return on equity = 𝑅𝑂𝐸

𝜎𝑅𝑂𝐸 , (2)

where the ROE is measured as the annualized net income as a percent of average total equity on a consolidated basis. For the standard deviation of the return on equity, the same time-frame is used as with the standard Z-score, following Lepetit and Strober (2013). A higher risk-adjusted return on equity ratio indicates better performance per unit of risk and higher banking stability (Lee & Li, 2012). Consistent with the literature on, the risk-adjusted returns on equity is used as an additional measure of performance, it is comparable with the Z-score and it is a quite common measure in the banking literature (Stiroh & Rumble, 2006; Sanya & Wolfe, 2011). The comparability is reflected in the high degree of correlation (0.553, see Table 2) between the Z-score and the risk-adjusted ROE. However, there are some differences. Risk-adjusted returns take into account the risk that the banks bear in earning profit, which is an advantage compared to the Z-score. Another difference is that this measure does not only take the banks insolvency into account but focus on profitability as well, which is also an important part of financial stability (Duménil & Lévy, 1992). However, the risk-adjusted return on equity

does not deal with the asset size problem and the assumption of the normality of returns.5 Still,

it can be seen as the best alternative due to the fact that other measures reduce the sample size significantly or do not measure the real impact of financial stability.

3.1.2 Systemic risk analysis

SRISK is a measure of systemic risk, developed by Acharya et al. (2012) and Brownlees and Engle (2016). SRISK stands for systemic risk and is defined as the expected capital shortfall

asset volatility is constant. The distance-to default model ignores the options-on-options nature of bank equity and debt.

5 The only measurement which solve this problem is the bank’s ratio of non-performing loans to total assets.

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15 of a financial entity conditional on a prolonged market decline (Brownlees & Engle, 2016). SRISK is a function of the size of the firm, its degree of leverage, and its expected equity loss. It measures the expected capital shortage faced by a financial firm during a period of system distress when the market declines substantially. Firms with the highest SRISK are the largest contributors to the undercapitalization of the financial system in times of distress. The sum of SRISK of all banks in an economy is a measure of overall systemic risk. In other words, SRISK is capital that a bank is expected to need when it faces a financial crisis. Hence, aggregate SRISK measures the total amount that the government will have to provide to bail out the financial system should a crisis occur (Brownlees & Engle, 2016). SRISK gained importance after the global financial crisis due to its predictive ability of capital injections. For example, SRISK shows the beginning of the eroding of capitalization in the financial system in July 2007, with a peak in SRISK for Lehman Brothers before declaring bankruptcy in 2008. The calculation of SRISK is based on balance sheet information and an appropriate LRMES estimator. The formula can be expressed as:

𝑆𝑅𝐼𝑆𝐾𝑖𝑡 = 𝑘𝐷𝑖𝑡 ⎼ (1 ⎼ k)𝑊𝑖𝑡(1 ⎼ 𝐿𝑅𝑀𝐸𝑆𝑖𝑡+ℎ|𝑡(𝐶𝑡+ℎ|𝑡)), (3)

where k is the minimum fraction of capital as a ratio of total assets that each firm needs to hold. This prudential capital ratio is equal to 8 percent, following Acharya et al. (2012) and Laeven

et al. (2016).6 Moreover, Brownlees and Engle (2016) conclude that the results are substantially

stable in a reasonable range of values of k. 𝐷𝑖𝑡 stands for the total liabilities which equal the

book value of the firm’s debt and 𝑊𝑖𝑡 represents the market value of equity. Further, LRMES

refers to the Long-Run Marginal Expected Shortfall, which will be explained below. Lastly, 𝐶𝑡+ℎ|𝑡 stands for the market decline, where h equals 180 days and the threshold 𝐶𝑡+180|𝑡 will be set to 40 percent, following Acharya et al. (2012) and Laeven et al. (2016). The threshold of -40 percent and 180 days are chosen because, according to Acharya et al. (2012), a crisis occurs

whenever a broad index falls by 40 percent over the next six months.7 For these scenarios, the

expected loss of equity value of firm i is called the LRMES. The LRMES incorporates the volatility of the firm and its correlation with the market, as well as its performance in extremes.

6 The 8% guideline has been chosen on historical content. The U.S. derivatives holdings are reported under the

Generally Accepted Accounting Principles (GAAP) principles, which reported derivatives holdings as net. In contrary, European institutions follow the International Financial Reporting Standards which reports their derivatives as gross. Therefore, Brownlees and Engle (2016) suggest a prudential capital ratio of 8% for U.S. banks and 5.5% for European banks.

7 This is based on the most pessimistic scenarios for the market returns. According to Acharya et al. (2012) the

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16 Hence, it is the average of fractional returns of the firm’s equity in crisis scenarios, which is expressed in the next equation.

𝐿𝑅𝑀𝐸𝑆𝑖𝑡+180|𝑡(𝐶𝑡+180|𝑡) = 1 ⎼ exp(⎼18 ∗ MES𝑖𝑡+180|𝑡(𝐶𝑡+180|𝑡)). (4)

Equation (4) shows that LRMES is based on the Marginal Expected Shortfall (MES) of one-day. The MES of a single firm is simply the derivative of the market’s expected shortfall with respect to the firm’s market share or capitalization (Idier et al., 2014). The MES of an institution can be defined as its expected equity loss when the market itself is in its left tail. This tail expectation of the firm’s equity return can be seen as the one-day loss expected if market returns are less than -2 percent (Acharya et al., 2016). From this, it implies that:

𝑀𝐸𝑆𝑖𝑡+1|𝑡(𝐶𝑡+1|𝑡) = ⎼𝐸𝑡(𝑅𝑖𝑡+1|𝑡|𝑅𝑚𝑡+1|𝑡 < C) , (5)

where 𝑅𝑖𝑡+1|𝑡 stands for one-day stock return for bank i and 𝑅𝑚𝑡+1|𝑡 denotes the one-day stock

of the market m. Finally, C is the threshold of the decline in the market index, which corresponds to -2 percent in this case (Acharya et al. 2012; Laeven et al., 2016). Hence, firms with more systemically risky assets will have a higher MES and must hold higher amounts of capital. The LRMES incorporates the risk of those underlying risky assets.

Following Laeven et al. (2016), SRISK data could contain negative values. The reason for this is that banks with large capital buffers could absorb systemic shocks relatively easy. Hence, they subtract systemic risk out of the system by, for example, acquiring the client base of a failing bank. Moreover, negative values of SRISK could provide meaningful information on the relative contribution of the bank to systemic risk.

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17 fits into this study. This study wants to measure the influence of the current banks’ derivatives holdings on the systemic risk for the coming period, not the previous one. An important characteristic of the SRISK approach is that it merges together balance sheets and market information to estimate the conditional capital shortfall of a firm. Therefore, SRISK is a forward-looking measure and is particularly suitable for measuring systemic risk.

3.2 Empirical Model

3.2.1 Individual bank risk model

To examine the effects of banks’ derivatives holdings on the financial stability in its widest sense, two regressions are used. This subsection focusses on the bank-level model. Hence, the stability of individual banks. The bank-level analysis is based on the following model:

𝑍 − 𝑠𝑐𝑜𝑟𝑒𝑖𝑡 = 𝛽1(𝐷𝐸𝑅)𝑖𝑡−1 + 𝛽2𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝑖𝑡 + 𝜔𝑡 + 𝛾𝑖 + 𝜀𝑖𝑡, (6)

where 𝑍 − 𝑠𝑐𝑜𝑟𝑒𝑖𝑡 is measured by the individual natural logarithm of the Z-score for bank i at

time t. Moreover, (𝐷𝐸𝑅)𝑖𝑡−1 is the measurement of a specific category of derivative security

of bank i as a share of its total assets at time t, following Ghosh (2017). This implies that when

𝛽1 is positive, that category of derivative security reduces the risk of individual banks, because

the Z-score inversely related to individual stability. Hence, a larger value the bank-level Z-score

means less overall bank risk and higher bank stability. The coefficient 𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝑖𝑡 stands for

several control variables, which will be explained in the next subsection. Furthermore, 𝜔𝑡 are

the time-fixed effects, 𝛾𝑖 the bank-specific intercept and 𝜇𝑖𝑡 stands for the error term for each

entity at time t.

According to Ghosh (2017) there might be an endogeneity problem. The reason for this endogeneity may be due to the fact that banks with higher risk will have a greater incentive to hedge using derivatives. Moreover, banks that are in a distressed situation could have a greater incentive to use derivatives for speculative positions in order to save themselves. Endogeneity refers to the problem that causality might run in both ways, from independent variable to dependent variable and vice versa. This endogeneity may cause biased coefficients. The explanatory variables of banks’ derivatives holdings are all lagged by one year in order to reduce the potential econometric concern of endogeneity (Ghosh, 2017). The literature do not lag the control variables used in this research, I choose not deviate from this.

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18 values of the explanatory variables as instruments. Moreover, Roodman (2009a) concludes that GMM approach is useful with relatively small time periods; when independent variables are not strictly exogenous and when there are fixed individual effects, heteroscedasticity and autocorrelation. For these reasons, I check the robustness of the empirical results with the

dynamic GMM panel regression.8 This will be done for equations (6) until (9).

Another robustness check is to use the risk-adjusted return on equity (ROE) as an alternative

measure for 𝑍 − 𝑠𝑐𝑜𝑟𝑒𝑖𝑡, which leads to the following equation:

𝑅𝑖𝑠𝑘 − 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅𝑂𝐸𝑖𝑡 = 𝛽1(𝐷𝐸𝑅)𝑖𝑡−1 + 𝛽2𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝑖𝑡 + 𝜔𝑡 + 𝛾𝑖 + 𝜀𝑖𝑡. (7)

The dependent variable 𝑅𝑖𝑠𝑘 − 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅𝑂𝐸𝑖𝑡 is the only difference from the previous

equation. Hence, the explanation of the other variables is the same as provided in Equation (6).

3.2.2 Systemic risk model

In order to test the hypothesis on the influence of banks’ derivatives holdings on the systemic risk, the following econometric model is used:

𝑆𝑅𝐼𝑆𝐾 = 𝛽1(𝐷𝐸𝑅)𝑖𝑡−1 + 𝛽2𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝑖𝑡 + 𝜔𝑡 + 𝛾𝑖 + 𝜀𝑖𝑡, (8)

where 𝑆𝑅𝐼𝑆𝐾 stands for the measurement of systemic risk; SRISK, which is the dependent

variable for systemic risk at bank i at time t. For the explanation of the other variables in this regression, see Equation (6). This study uses LRMES as an alternative measure for the systemic risk contribution. Different measures could complement each other to provide a robust diagnostic of the systemic risk contribution (Mayordomo et al., 2014). Hence, the LRMES is used as a robustness check for the measurement of systemic risk, using the following equation:

𝐿𝑅𝑀𝐸𝑆 = 𝛼𝑖 + 𝛽1(𝐷𝐸𝑅)𝑖𝑡−1 + 𝛽2𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑠𝑖𝑡 + 𝜔𝑡 + 𝛾𝑖 + 𝜀𝑖𝑡. (9)

The dependent variable 𝐿𝑅𝑀𝐸𝑆 is the only difference from the previous equation. Hence, the explanation of the other variables is the same as provided in equation (6).

Lastly, this analysis separates the pre- and post-crisis time period, from 2000–2007 and 2008–2017 respectively. This has been done in order to check whether the results remain robust after the financial crisis and to grant better insight on the effects of bank’s derivatives holdings on the financial stability, and whether the financial crisis changed this relationship. I use a

8 According to Samarina and Bezemer (2016), the system GMM estimator does not solve the endogeneity

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19 dummy variable that takes the value 1 for the pre-crisis period and 0 otherwise. This will be done for both bank and country-level.

3.3 Control variables

There are other variables that influence the stability of banks and its contribution to systemic risk. Researchers have studied the determinants of financial stability in its widest sense using a variety of models and explanatory variables (Capelle-Blancard, 2010). A number of variables are used in the equation estimations for robustness purposes and to assess the strength of the link between the banks’ derivatives holdings and financial instability.

This study includes the following bank-specific control variables: bank’s total assets, loan-to-assets ratio, the net interest margin, noninterest expense to average assets, and the loan loss provisions to total assets (LPP ratio). This study will not follow (Ghosh, 2017) for the country controls like GDP per capita because section 4.3 illustrates the need for time-fixed effects, which are sufficient to control for country-wide business cycle effects when researching one country (Buch & Schlotter, 2013).

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20 a relative high loan-to-assets ratio may be at greater risk (Goddard et al., 2013). On the other hand, when the loans-to-assets ratio is interpreted as lending specialisation, a high ratio could indicate that a bank specialises in lending because it may reduce intermediation costs and enhance profitability (Goddard et al., 2013). Third, the net interest margin, which exists of the total interest income minus total interest expense as a percentage of average earning assets. It is a measure of profitability, which is expected to have a positive effect on financial stability (IJtsma et al., 2017). Fourth, the non-interest expense to average assets. This is measured as salaries and employee benefits, expenses of premises and fixed assets, and other non-interest expenses as a percentage of average total assets (FDIC, 2018). Non-interest expense to average assets measures the bank’s effectiveness in controlling its operating expenses. A higher ratio means higher inefficiency, hence it is expected to negatively affect financial stability. Fifth and last, the ratio of loan loss provisions to total assets is a measure of credit risk and loan-portfolio quality, which can also be interpreted as an ex-ante measure of the level of expected losses (Berger et al., 2010). Moreover, it is used in the literature to measure output quality in the way in which managers invest in high-risk assets (Fu et al., 2014). This ratio is expected to have a negative effect on financial stability (Uhde & Heimeshoff, 2009).

Since the loan-to-assets ratio, net interest margin and loan loss provisions to total assets are all defined as percentages, they are included without a logarithmic transformation.

4. DATA

4.1 Sources and sample

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21

Figure 1: different classes of derivatives, derived in Trillions of U.S. dollars. Source: FDIC.

In order to analyse the behaviour regarding the bank’s derivatives holdings and their influence on the financial stability in the United States, micro-level (i.e. balance sheet, income statement, control variables) data is collected from the Federal Deposit Insurance Corporation (FDIC) database. The only exception to this is the data of the dependent variables of systemic risk; the SRISK and LRMES. Table A1 in Appendix A provides an overview of the variables and their definition and data sources. The choice of the FDIC database has been made based on its reliable reputation as one of the most extensive and widely-available databases for U.S. banks. Moreover, this database is used by most researchers who conducted research on banks’ derivatives holdings (Ghosh, 2017; Zhao & Moser, 2017). The FDIC depends on data provided by individual banks. Banks could engage in window dressing behaviour, which could lead to a bias in the results and could go at cost of the reliability of the data. However, the FDIC cooperates with the U.S. government to perform audits, standard procedures, internal and external controls to increase the reliability of the data.

The data availability is an important reason to focus on the U.S. derivatives market. The FDIC database is the only database that provides such an extensive and comprehensive database with detailed information on derivatives and its underlying classes. Other databases, like Orbis bank focus or Thomson Reuters DataStream, only provide data on aggregate or credit derivatives. Hence, an extensive and detailed research on banks’ derivatives holdings and their influence on financial stability could only be accomplished in the U.S. with the FDIC database. Besides this, the U.S. derivatives market is an interesting market to investigate, because it is the largest market for derivative holdings due to its tremendous growth after the Gramm–Leach– Bliley act. The FDIC database provides bank-level data for over 5,500 U.S. banks.

0 50000 100000 150000 200000 250000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017

Different classes of derivatives (in Trillions of $)

Credit derivatives Interest-rate derivatives

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22 The system-wide data on systemic risk is provided by the Volatility Laboratory of the Volatility Institute, which was created at the New York University Stern School of Business. The Volatility Laboratory provides real-time measurement and modelling of financial volatility and correlations for a wide spectrum of assets. This study uses the SRISK and the LRMES measures of the Volatility Laboratory, which are present for 155 U.S. firms. However, this research focusses only on U.S. banks, forcing me to reduce my sample to 50 U.S. banks, which are matched with the FDIC database. These are all currently active banks. Table A2 in Appendix A provides a complete overview of all banks involved in this study. This research may contain a selection bias towards large banks. For the systemic risk analyses, banks are selected that trade on a reasonably frequent basis, which are more often large banks. Moreover, the Volatility Laboratory focusses primarily on larger firms (both in terms of total assets and market capitalization) because larger firms will typically pose more of a threat when it comes to SRISK. This limits the extent to which the sample is representative for all U.S. banks. However, because the sample covers a large part of the population of interest, (i.e. over 62% of total assets 2017 and over 96% of total derivatives holdings in the FDIC database), one can still speak of a decent representation.

Ideally, the starting date of this research would be November 1999, the start of the Gramm– Leach–Bliley Act. However, due to data availability of the Volatility Laboratory of the Volatility Institute the starting date will be dictated by data availability. Therefore, the period of analysis is 2000-2017. Hence, the time-span is a few months after the start of the Gramm– Leach–Bliley Act. and until as recent as possible in order to fill the gap in the existing literature. In this timespan, some events may have occurred that disrupt the regression results. The timespan should be large enough to marginalize most of the disturbing effects. However, the financial crisis did have a significant impact on various economic variables (Broccardo et al., 2014; Li & Marinč, 2014; Keffala, 2015). Therefore, this study compares the relationship between banks’ derivative holdings and financial stability after the crisis period (2008–2017) with the pre-crisis one (2000–2007) in order to verify whether the results obtained are robust.

4.2 Summary statistics

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23 Most of the variables have data available for all years (2000–2017) and for each bank (N = 50). However, the data on the interest-rate, exchange-rate and commodity and equity derivatives is not available for the whole sample. Some banks do not hold all classes of derivatives in the whole sample period. Moreover, not all banks have data available for the whole sample period, due to mergers or acquisitions. Due to these two reasons, the panel dataset is unbalanced. This can lead to a reduced statistical power of the analysis. Nonetheless, for all data over 95% is available and a minimum of 760 observations per variable divided over 50 U.S. banks should be enough to derive a panel regression because it is closely related to the rule of thumb of 15 observations per variable.

Table 1: Descriptive statistics of the variables

Obs. Mean St. Dev. Minimum Maximum

Z-score 794 20.41 14.05 0.81 96.60 Return on Equity 794 2.23 1.66 -3.45 7.99 SKRISK a 794 2,058 25,516 -254,278 142,972 LRMES 794 45.30 11.75 8.27 83.94 Credit derivatives a 794 170,639 810,265 0 8,391,629 Interest-rate derivatives a 761 2,841,332 10,173,180 0 69,897,680 Exchange-rate derivatives a 760 439,845 1,571,049 0 11,504,330

Commodity and equity derivatives a

760 58,809 287,179 0 2,664,154

Total assets a 794 148,775 354,568 291.54 2,140,778

Loan-to-assets ratio 794 57.87 19.21 1.86 95.52

Net interest margin 794 3.35 1.15 -0.50 9.28

LPP-asset ratio 794 0.38 0.64 -0.42 5.70

Non-interest expense to average assets

794 2.87 2.15 0.15 28.71

Notes: For definition of variables, see Table A1. a Expressed in millions of U.S. dollars.

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24

Table 2: Pair-wise correlation between variables

1 2 3 4 5 6 7 8 9 10 11 12 13 1 Z-score 1.000 2 Return on Equity 0.553 1.000 3 SRISK -0.041 -0.128 1.000 4 LRMES -0.190 -0.360 0.298 1.000 5 Credit derivatives 0.057 -0.052 0.495 0.166 1.000 6 Interest-rate derivatives 0.045 -0.062 0.486 0.179 0.625 1.000 7 Exchange-rate derivatives -0.057 -0.092 0.329 0.187 0.501 0.559 1.000 8 Commodity and equity derivatives 0.101 0.014 0.361 0.087 0.555 0.563 0.332 1.000 9 Total assets -0.158 -0.237 0.320 0.231 0.368 0.509 0.333 0.451 1.000 10 Loan-to-assets ratio -0.082 -0.031 -0.219 -0.134 -0.291 -0.319 -0.444 -0.251 -0.273 1.000

11 Net interest margin 0.041 0.161 -0.168 -0.104 -0.262 -0.226 -0.428 -0.200 -0.235 0.616 1.000

12 LPP-asset ratio 0.248 -0.309 0.089 0.266 -0.002 0.002 0.090 -0.007 0.101 0.223 0.343 1.000

13 Non-interest expense to average assets

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25 are tested in separate models, therefore this is of no concern. The vital derivatives variables have been tested using the variance inflation factor (VIF) test. This test quantifies how much the variance is inflated and helps to identify multicollinearity.9 The average VIF of the derivatives variables is 3.57. According to Curto and Pinto (2011), this is a low correlated predictor and further measures for multicollinearity are not necessary. Moreover, the VIF for individual classes of derivatives remain well below the rule of thumb of 10 that is commonly used to identify excessive multicollinearity (O’Brian, 2007). The results of the VIF test are displayed in Table B1 in Appendix B.

4.3 Panel data assumptions

Before I can commence with the regression analyses using the abovementioned data, certain assumptions need to be tested and analysed. The results of the panel-data assumptions tests are displayed in tables B2 to B9 in Appendix B. A graphic form of the results is displayed in Appendix C. The model for both equations (6) and (7), with the Z-score and risk-adjusted ROE as dependent variables, and for equations (8) and (9), with SRISK and LRMES as dependent variables, are estimated using a fixed-effects regression. The reason for this lies in the results of the Breusch-Pagan Lagrange multiplier and the Wooldridge Hausman test. The outcome of the Breusch-Pagan Lagrange multiplier test (Table B2) makes clear that I should reject the null hypothesis of zero variance across entities. Hence, a pooled OLS regression is not appropriate in this case. Next, the Wooldridge Hausman test (Table B3) decides whether the differences between the coefficients are systematic. This test helps to decide between fixed or random effects. The null hypothesis can be rejected, which means that the differences between coefficients are systematic, which indicates the need for fixed effects. The fixed-effect model allows for different intercepts for different banks and thus controls for unobserved characteristics of banks. This is an important advantage of the fixed-effects model. Furthermore, standard errors in all regressions are clustered to correct for both autocorrelation and heteroscedasticity, which are present in this sample (see tables B4 and B5). Moreover, I

conduct a test to check whether there is a need for time-fixed effects.The null hypothesis of the

test is rejected in all equations, which indicates the need for including time-fixed effects (Table B6). Time-fixed effects into account take yearly trends that would otherwise be captured by the estimated residuals. Moreover, I ran a Pesaran cross-sectional dependence test ascertain whether the residuals are correlated across entities (Table B7). I do not find evidence for

9 I have used a hand-written Stata program (Phil Ender’s Collin) to derive to VIF because the normal VIF is only

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26 rejecting the null hypothesis and therefore conclude that there is no contemporaneous correlation. Hence, there is no need to use Driscoll and Kraay standard errors (Hoechle, 2007).

Stationarity is an important condition. Unit roots could lead to spurious regressions, which make estimates unreliable (Coe & Helpman, 1995). I conducted a Fischer-type unit-root test based on the augmented Dickey-Fuller test because this test is compatible with an unbalanced panel. According to Levin et al. (2002), unit-root tests based on the Dickey-Fuller test can achieve high substantial power with a panel of moderate dimensions (i.e. N = 25 and T = 25),

which is similar to the sample in this study (N = 50; T = 18).10 The null hypothesis of a unit

root is rejected for Z-score, risk-adjusted ROE, and LRMES at the 1% level and for SRISK at the 5% level (Table B8). Hence, I can proceed under the assumption of stationarity that is necessary for applying the central limit theorem. However, the Fischer-type unit-root rest is very likely to reject the null hypothesis of all panels containing unit roots (Coe & Helpman,

1995). Therefore, the augmented Dickey-Fuller test is conducted for each bank separately.The

results provide evidence that some bank-specific panel might be stationary.11 For this reason,

this study provides a robustness check in order to understand how this possible non-stationarity influences the results.

The Shapiro-Wilk normality test is performed to ascertain whether the dependent variables, derivatives, or residuals of the regression results are normally distributed (see Table B9). The null hypothesis that the data is normally distributed is rejected in all cases, which indicates that the data could be non-normal. However, Ghasemi and Zahediasl (2012) conclude that the Shapiro-Wilk test generally leads to a rejection of the normality assumption for a sample size greater than 50. To check whether the distribution is actually non-normal, histograms are constructed for the dependent variables and the residuals of the regression results of equations (6)-(9) (see figures C1 and C2 in Appendix C). The histograms in Figure C1 demonstrate that the Z-score is only normally distributed after a logarithmical transformation. Moreover, I conclude that the risk-adjusted ROE and the LRMES are approximately normally distributed. The same results apply for the residuals of these variables, as can be seen in Figure C2. The only problem lies within the SRISK measure and its residuals, based on Equation (9). The

SRISK is leptokurtic and contains a few outliers.12 The last normality check is to illustrate the

10 The literature is inconclusive whether to use a Fischer-type unit-root test based on augmented Dickey-Fuller

or on Phillips-Perron (which is also appropriate with this sample size and time-frame). Both of these methods have their advantages and disadvantages (Kwiatkowski et al., 1992). The results do not show significant differences. Therefore, I only show the test based on the augmented Dickey-Fuller statistic.

11 The power of these test is lower than when providing the full sample (Coe & Helpman, 1995). However, it still

can be useful to run these test in order to rule out the possible problem of stationarity.

12 According to Martín et al. (2012) the presence of leptokurtosis is common in most financial data. Leptokurtic

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27 quintile-normal plots, which examine non-normality in the extremes of the data (see Figure C3). This test plots quintiles of residuals against quantiles of a normal distribution (Torres-Reyna, 2006). Non-normality of the errors will have some impact on the precise p-values of the tests on coefficients. But if the distribution is not to a great extent non-normal, the tests still provides solid approximations (Hanusz, Tarasinka & Zielinski, 2016). The graphs demonstrate that the tails are relatively normal, only the SRISK measure is slightly non-normal. This can be caused by the outliers of a few banks in some years. The last graphical test is the scatterplot of the derivatives versus the dependent variables Z-score and SRISK (see Figure C4). This test also supports the evidence for the existence of outliers in this sample.

The literature is inconclusive on how to deal with extreme values. I choose to use the winsoring procedure to adjust for outliers in the data. Winsorization is a widely accepted methodology for reducing skewness and kurtosis (Shete et al., 2004). The reason to choose for winsorizing is that it ensures that the results are not be driven by outliers, without missing out information. Moreover, according to Kennedy et al. (1992), the winsorizing procedure produces a regression model that fits the data well and has a low level of prediction error. For this reason, I estimate the models for equations (6), (7) and (9) on winsorized data as a robustness check, where the variables are winsorized at the 1% level at both tails. Moreover, the model for Equation (8), with SRISK as dependent variable, contains winsorized data only, because the outliers could be a too large problem and might bias the results. Figures C1 and C2 shows the effect of winsorized data on the histograms. After winsorizing, the data is more normally distributed. Moreover, when the sample size is large enough (> 30 or 40) a small violation of normality assumption should not cause major problems because the distribution tends to be normal, regardless the shape of the data (Ghasemi & Zahediasl, 2012).

A drawback of the fixed-effects estimation is that fixed effects appear in the error term and are generally correlated with one or more right-hand side variables when there exists endogeneity. The present study assumes there is no endogeneity. But since the literature does not rule out the possibility of nuisance effects due to endogeneity. Keffala (2015) concludes that the GMM estimator technique is a useful approach to account for possible endogeneity. Banks’ derivatives holdings could depend on their own past values. The GMM estimation deals

with this problem by using instrumentsfor the first-differenced equation which are then tested

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28 order to test whether the overidentifying restrictions are valid.13 The results of the GMM assumption tests are incorporated in the regression results of Table D2 in Appendix D. The null hypothesis cannot be rejected for the equation with the Z-score, SRISK and risk-adjusted ROE as dependent variables. Meaning that those error terms are not correlated with the instruments. However, I can reject the null hypothesis for LRMES, which indicates that the validity of these estimates have to be interpreted with caution. (Baum, 2007). Second, according to Arellano and Bond (1991), the model should be tested for autocorrelation of the second-order AR(2). When second-order autocorrelation is present, the probability of correlated errors in subsequent years is very high. Table D2 illustrates that there is no sign of autocorrelation. Hence, the validity of the lagged instruments is sufficient. The two-step procedure is used, which uses the residuals

from the one-step variant estimates and is asymptotically more efficient (Roodman, 2009a).14

Moreover, Windmeijer (2005) standard errors have been used to account for the downward biased problem due to the large numbers of instruments and to account for panel-specific autocorrelation and heteroscedasticity. Last, Roodman (2009b) concludes that too many instruments can lead to overfitting of the endogenous variables and lead to a loss of power. The rule of thumb is keep the number of instruments below the number of observations. For this reason, I limit the number of instruments by restricting the number of GMM-style instruments to 2.

5. EMPIRICAL RESULTS 5.1 Main results

This section describes the main empirical results of the analysis of model equations (6) and (7). The main results focus on the complete dataset with the Z-score and SRISK as dependent variables. Robustness checks are conducted to divide the dataset into the pre- and post-crisis period. Furthermore, analyses will be controlled with alternative measures of both individual and system-wide stability.

Table 3, which is based on Equation (6), shows the regressions results for the annual fixed-effects model. The results are used to answer the first hypothesis, stating that all classes of banks’ derivatives holdings increase the financial stability of individual banks. The results are partially consistent with the first hypothesis that there is a significant effect of bank’s

13 The Sargan-Hansen test checks the instrument validity where the null hypothesis states that the instruments

are exogenous (Roodman, 2009b). Instrumental variables could be powerful, but when the null hypothesis is not rejected then the validity of the estimates in strongly doubted. Hence, the higher the P-value the better because this indicates a compatible sets of instruments.

14 This study uses the Arellano-Bond estimation (Arrelano & Bond 1991). In the Arellano–Bond method, first

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29 derivatives holdings on individual stability. The number of observations is lower than in Table 1 due to the lagged derivatives variables.

Table 3: Empirical analysis results for financial stability of individual banks Z-score (log) Model (1) Robust-cluster Z-score (log) Model (2) Robust-cluster Z-score (log) Model (3) Robust-cluster Credit derivatives t-1 0.0225 * (0.0119) 0.0250 ** (0.0104) 0.0242 ** (0.0104) Interest-rate derivatives t-1 0.0013 (0.0036) 0.0034 (0.0029) 0.0021 (0.0034) Exchange-rate derivatives t-1 –0.0179*** (0.0023) –0.0187 *** (0.0019) –0.0172 *** (0.0018) Commodity and equity

derivatives t-1 –0.0285 (0.0834) –0.0818 (0.0731) –0.0356 (0.0780)

Total assets (log) –0.0766

(0.0679) –0.0665 (0.0666) –0.0577 (0.0657) Loan-to-assets ratio 0.0043 ** (0.0019)

Net interest margin 0.0843 ***

(0.0213) LPP-asset ratio –0.0312 * (0.0153) –0.0487 ** (0.02350) Non-interest expense to average assets –0.0302 *** (0.0032) –0.0350 *** (0.0035) Number of observations 710 710 710 Numbers of banks 50 50 50

Time-fixed effects Yes Yes Yes

Bank-fixed effects Yes Yes Yes

Adjusted R2 0.14 0.28 0.25

F 69.83 *** 73.61 *** 96.20 ***

Notes: For definition of variables, see Table A1. Clustered standard errors in parentheses. Time-fixed effects are not reported. *** p < 0.01, ** p < 0.05, * p < 0.1.

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30 and includes the net interest margin, whereas model 3 includes the loan-to-assets ratio and excludes the net interest margin.

According to the data in all columns of Table 3, there exists a positive relationship between banks’ credit derivatives holdings derivatives and financial bank stability, which remains significant at a 5% level. When the ratio of credit derivatives to its total assets increases with 1 unit, this increases the Z-score with approximately 2.5%, with corresponding 95% confidence

interval [0.4, 4.59]%.15 This implies that when credit derivatives on the bank balance sheet rises

(as a percentage of total assets) the bank becomes more solvent (i.e. less overall risk, higher stability), as the Z-score is an inverse measure for default risk. The coefficient is large enough to speak of a serious economical significant impact.

Another remarkable finding is that a bank’s holdings of exchange-rate derivatives reduce the financial stability of banks, which goes against the first hypothesis. The impact of a 1 unit increase in the holdings of exchange-rate derivatives divided by total assets decreases the Z-score by approximately 1.87%, with corresponding 95% interval [-2.26, -1.33]%. This result is significant at a 1% level for all columns. This effect is also economically important.

The results in Table 3 imply that the holding credit derivatives increases the financial stability of banks, whereas holding exchange-rate derivatives by banks decreases financial stability. As shown in the literature section, derivatives could be used for either positive risk-hedging instrument or speculative purposes. The results of this regression would indicate that credit derivatives are more often used for hedging risk, due to its positive effect on financial stability. Exchange-rate derivatives reduce finance stability and therefore the results indicate that exchange-rate derivates are more likely to be used for speculative purposes, explaining the negative relationship with financial stability. Although the literature mentions several purposes of derivative holdings as such, there is no explanation of specific uses of the different classes of banks’ derivatives holdings and why there would be differences among the classes of derivatives. More research is needed to provide theoretical explanations for these results.

Table 3 does not provide significant results for the interest-rate and commodity and equity derivatives. It could be the case that interest-rate derivatives and commodity and equity derivative are both frequently used for speculative and hedging purposes, which diminishes the significance for either a positive or a negative effect on financial stability. It could also be the case that the sample size needs to be enlarged in order to find significant results, which indicates the need to broaden the extensive database to other countries. Anyway, further research is

15 This is a log-linear function, meaning that if we change X by 1 (unit) this leads to (approximately) a 100 ß1%

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