The effect of fair value derivatives estimates on risk levels of US banks

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The effect of fair value derivatives estimates on

risk levels of US banks.

MSc Quantitative Finance Thesis

Academic Year 2017/2018

Igor Lipinski, 10630406

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Statement of Originality

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

I declare that the text and the work presented in this document are 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.

Abstract

In this paper I investigate the relation between fair value derivatives positions and risk level of 130 large US banks for the period of 2001-2016. The analysis also looks at the pre- and post-crisis period to analyze the differences between the two. The findings are generally consistent with research conducted using notional amounts as derivates are negatively correlated with risk and the effects in the post-crisis period are either insignificant or weaker than in the pre-crisis period. However, several differences exist and the magnitude of said effect also generally differs from the existing research which suggests that more extensive research into the differences between notional amounts and fair value positions should be conducted to highlight the different ways in which the two methods reflect risks involved in derivatives trading and whether the fair value method indeed provides extra benefits compared to notional amounts reporting.

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1. Introduction

Financial institutions such as banks and bank holding companies engage in derivative activities for two main reasons, hedging and speculation. Both of these purposes lead to derivatives having impact on the risk levels of banks, either negative or positive. While financial companies use derivatives primarily as a risk management tool, the trends are significantly different in the banking industry. While the vast majority of banks uses financial derivatives, e.g. 90% of Italian banks report derivative usage (Broccardo, Mazzuca & Yaldiz, 2015), the motivations behind derivatives use remain unclear and it remains challenging to verify the extent of hedging with derivatives in the banking industry.

In the last 30 years the market for derivatives has seen a massive expansion, with the notional amounts surging upwards and new types of instruments being introduced regularly. Credit derivatives, a fairly recent addition to the market, have seen their notional amounts double every year between 2001 and 2006, reaching $35 trillion at the end of 2006. (Gibson, 2007) Despite this meteoric rise, the impact of derivatives on risk levels remains unclear. While the simpler derivatives are well understood, instruments such as CDOs still pose a significant challenge to those attempting to evaluate them, leading to companies suffering great losses due to lack of understanding of the underlying risk exposure. In 2001, the Financial Times reported that American Express lost “hundreds millions of dollars” due to failed investments in CDOs, as a result of keeping the first-loss tranches of those CDOs, which contain a great deal of risk. The CEO of the company later admitted that his company did not fully understand the exposures they were facing. This was not the only failure of 2001, as Enron Gas Services suffered $1.2 billion losses as a result of their derivative activities, forcing the corporation to file for bankruptcy (Yang, et al., 2006). Other notable examples of losses due to derivatives include Gibsons and Greeting, Procter and Gamble and Baring PLC.

These circumstances created substantial uncertainty surrounding derivatives, both among the market participants and international regulators, who grew especially concerned of banks’ involvement in derivatives trading as the risk reduction they offered was put into question. As a response, many regulations were introduced and disclosure requirements for banks using derivatives tightened to ensure transparency of banks reporting their derivatives positions. However, one of the main problems was the measurement used in reports, as the notional amounts reported by banks often fail to fully reflect the risk that is involved and moved around in such a transaction, which raised doubts about its reliability despite the ease of collecting such data.

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5 United States were at the forefront of this push, issuing multiple Statements of Financial Accounting Standards which reinforced the Generally Accepted Accounting Principles: SFAS 105, 107, 109, 119 and 133. SFAS 107 is of particular interest here as it attempted to combat the inefficiencies of reporting notional amounts by imposing a new method of reporting derivatives positions, known as fair value. The Financial Accounting Standards Board considers the fair value to be a relevant measure of the present value of net future cash flows from the derivatives that reflects assessments of both risks and returns.

Since the expansion of derivatives markets and the concerns surrounding their risk mitigating effects, multiple studies were conducted to test the correlation of risk levels of banks and their derivatives positions. Dai & Lapointe (2010) researched the effects of derivatives on asset risk of Canadian banks, Yang, et al. (2006) investigated the banking sector of South Korea, while Ghosh (2017) looked at the financial industry of United States. However, existing research is conducted almost exclusively using notional amounts of derivatives held by banks, as the data is easily available, while many countries do not impose fair value reporting on banks. In this paper, I aim to fill this gap in existing literature by testing the effects of fair value estimates of derivatives on the risk levels of US banks. Banks in the United States are required to report fair values of derivatives, which are also widely considered to be more reflective of the underlying risk of derivatives transactions, so using fair value estimates in testing the effects of derivatives on risks is an obvious decision. As such, my tests will investigate whether the fair value estimates provide significantly different results to those obtained while using notional amounts, when analyzing risk levels of banks. In a similar vein to Ghosh (2017) I also investigate the pre- and post-crisis periods as the risk profiles of banks in these two periods should be significantly different, and thus serve as an excellent field to verify whether fair values truly reflect derivative risk in a better way. The main contribution of this paper is thus to lay down the groundwork for the shift from using notional amounts to fair value estimates of derivatives in future research.

My results show that interest rate derivatives successfully reduce risk leading up to the crisis, while they’re inefficient at reducing risk after 2008. Earnings volatility is, however, not affected by fair value estimates, which confirms suspicions of managers that the new reporting method will results in higher earnings volatility being reported. In the pre-crisis period, the interest rate derivatives also increase bank profits, indicating that banks perform well in regards of managing their exposures. Other derivatives type do not significantly affect risk levels, mainly due to being relatively unpopular, however, exchange rate derivatives help reduce

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6 earnings volatility, showing that banks hedge foreign activities efficiently.

The rest of the paper is structured as follows: Section 2 reviews the literature relevant to the topic, explaining how and why banks manage risk, the rationale behind introduction of fair value accounting and investigating existing studies on the effects of derivatives on bank risk. Section 3 explains the methodology used in the analysis and provides detailed description of the dataset along with detailed descriptive statistics. Section 4 presents the results of the tests conducted on the main sample and subsamples, as well as analyzes the results and relates them to existing literature. Section 5 summarizes the paper, while providing concluding remarks and ideas for future research.

2. Literature Review

2.1 Why do banks manage risk?

In order to understand how derivatives can impact the risk levels of bank, we need to understand why banks engage in risk management in the first place. The business provided by commercial banks is inherently risky, as the various financial services provided by banks lead them to facing different types of financial risk. Since 1990 a lot of academic research on the topic was conducted, leading to a much better understanding of where commercial banks fir within the financial sector. (Santomero, 1997) As such, we know that majority of the risks banks face comes from items found on their balance sheet and these risk have remained the main focus of risk management and the discussion surrounding it.

Based on standard economic theories, value maximizing banks strive to maximize expected profit, while disregarding any variability around that expected value. However, other rationales exist that make active risk management a tempting prospect for banks to explore. Among these are managerial self-interest, and existence of imperfections that are not accounted for by theory such as nonlinearity of tax structure, financial distress costs and flawed capital markets. All these are valid reasons for banks to be concerned over return variability and thus encourage risk management.

Banks recognize that they do not need to take on unnecessary risk, and thus use different techniques to ensure that as much risk as possible is removed from their balance sheet activities such as lending, instead of taking on all of it. Many of the risks involved in transactions can be mitigated by good business practices and some of the other exposure can simply be transferred away to other parties by adjusting the offered products. Generally, banks should only manage risk that they can handle more efficiently than the market, namely, those that are a unique to the

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7 services provided by the banks.

Many common practices can be used to avoid risk at a base level, including the standardization of process, constructing diversified portfolios and designing compatible contracts. The first step prevents inefficient financial decisions, the second reduces possible losses and the first ensures proper practices by employees and the management.

Moreover, there are existing markets for many of the risk attributable to banks’ activities, which can help with transferring the exposures. (Santomero, 1997) Swaps and other derivatives can be used to shed interest rate risk, banks can change the borrowing terms or trade in financial claims to diversify risks embedded in their services. If the financial risks that banks face are understood by the market, the assets bearing those risks can be sold at their fair value, thus banks should not hold on to risks unless they possess a comparative advantage in managing them.

One example of such assets are those that contain very complex risk that would be difficult to communicate to the market, such as proprietary assets with narrow secondary markets. In such cases it might simply be less costly to hedge the risks yourself than transferring them to other market participants. Additionally, revealing such sensitive information to the market can give competitors advantage over the bank.

Another case where banks are willing to hold on to risks are positions where these risks are accepted because of the expected return they bring along. Credit risk is strictly tied to banks’ lending activities, as is market risk to trading in certain markets. These risks are absorbed by financial institutions and monitored closely, in order to successfully achieve their financial goals.

According to Santomero (1997), banks use a sequence of steps to ensure that their risk management programs are adequate and efficient. The sequence consists of four parts, those being standards, position limits, investment strategies and incentive contracts. These tools are tuned to efficiently measure and manage exposures that banks face, by limiting positions to reasonable levels while encouraging managers to handle risk in a manner that is consistent with the goals of the company.

Moreover, other authors identify additional channels in which risk management can enhance firm value. Froot, Scharfstein, and Stein (1993) find that risk management can improve planning and funding of future investments. Stulz (1990) shows that managing risk can improve tax benefits from debt financing while Brown (2001) points out that hedging reduces

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8 information asymmetries between the firm and stakeholders. Finally, DeMarzo and Duffie (1991) state that risk management reduces noise, which allows investors to identify the most skilled managers efficiently.

2.2 The expansion of derivatives markets and regulatory changes

While banks can utilize different on- and off-balance sheets activities to manage their risks, derivatives are becoming more and more dominant as the primary tool used for risk management. This shift results from managers viewing these financial instruments as the most efficient method of reducing risk. Moreover, banks may enter into the derivatives market in other roles, such as dealers or speculators. The explosive growth of the derivatives market indicates its importance as a risk management tool, particularly for financial institutions. However, such quick expansion raised concerns from analysts and regulators about the true impact of derivatives on the risks that banks face.

Yang, et al. (2006) point to Enron Gas Service’s failure in derivatives trading as one of the reasons for the debate on the real effect of derivatives on risk levels emerging. This has also risen many concerns from international regulatory bodies, leading to many regulations being issued with the aim of reinforcing the disclosure of derivatives exposure of financial institutions.

In the United States, SFAS 105, 'Disclosure of Information about Financial Instruments with Off-Balance-Sheet Risk and Financial Instruments with Concentrations of Credit Risk', and SFAS 107, 'Disclosures about Fair Value of Financial Instruments', were issued in March 1990 and December 1991, respectively. (Venkatachalam, 1996)

SFAS 105 greatly expanded the reporting standards for derivatives that applied to banks. Financial institutions had to report the notional amount of derivatives they hold along with the nature of these holding, that is trading or hedging, and disclose the credit risk contained in these instruments as well as concentrations of risk of all financial instruments.

Meanwhile, SFAS 107 required banks to report fair value estimates, where practical, for all financial instruments, whether these are recognized or not in the financial statements. This indicated that FASB considered these fair value instruments as a measure that accurately reflects the present value of future cash flows in terms of both risks and returns, particularly for the unrecognized financial instruments.

However, the articles included in SFAS 107 were quite unprecise and thus resulted in the disclosures of derivatives often being ambiguous. Venkatachalam (1996) analyzed annual

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9 reports from 1993 and found that banks reported these amounts in ways that made it difficult to distinguish whether the derivatives were held for trading or risk managements and whether they represented a net asset or liability.

In order to reinforce these regulations and force companies to provide more accurate reports, the SFAS 119 was introduced, tuning the rules in SFAS 105 and SFAS 107. SFAS 105 was amended with paragraph 14 of SFAS 119 by the following additions:

a. The disclosures under SFAS 105 (i.e., the extent, nature, terms, and credit risk of financial instruments with off-balance sheet OBS) risk) are extended to all derivative financial instruments including instruments without OBS risk under the purview of SFAS 119, and

b. The disclosures shall distinguish between financial instruments held or issued .,lot trading purposes and financial instruments held or issued ./'or purposes other than trading (emphasis added).

While the SFAS 107 was altered by paragraph 15 with the following articles:

a. The fair value disclosures under SFAS 107 (as applied to off-balance sheet derivatives) shall clearly indicate whether the fair value and carrying amount of financial instruments represent assets or liabilities (emphasis and parenthesis added),

b. Such disclosures shall distinguish between financial instruments held or issued for trading purposes and financial instruments held or issued for purposes other than trading (emphasis added), and

c. Entities shall not aggregate or net the fair value of derivative financial instruments with other derivative/non-derivative financial instruments except as permitted under FASB Interpretation No. 39, Offsetting of Amounts Related to Certain Contracts (emphasis added).

However, the fair value reporting was opposed by many companies who grew concerned about the complexity of these new rules. (Lins, Servaes, & Tamayo, 2011) They argued that this excessive complexity would bring in additional costs and also lead to increased earnings volatility being reported. Moreover, companies could face indirect costs resulting from the investors’ perceptions of the rise in volatility. Revsine, Collins, and Johnson (2002) suggest that managers could be faced with a decision between achieving better economic results by hedging with tools that address the real financial risks and using less efficient risk management methods to minimize the volatility.

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10 The extent to which the variability in earnings can increase relies on whether a given position qualifies for hedge accounting. Under this approach, if the derivative is perfectly correlated with the underlying exposure, so that both move together in response to market changes, there will be no effect on net income. (Lins, Servaes, & Tamayo, 2011) To achieve hedge accounting, firms need to prove that such high correlation exists, however, many companies employ effective hedging strategies that do not rely on a high correlation of the exposure and its hedge. Brown and Toft (2002) show that firms can frequently efficiently hedge their exposures using non-linear payoffs with instruments such as exotic option contracts. In these approaches, it is very challenging to prove the correlation between the underlying exposure and the instruments used to hedge it.

2.3 Existing research on derivatives’ effects on risk

As pointed out by Shiu & Moles (2010), the derivatives usage by corporations has received a lot of attention by researchers, leading to a very good understanding of corporate motivations for engaging into derivatives activities. The evidence found in the research points to financial risk management being the key driver for corporate use of derivatives. Looking at literature concerning non-financial firms, the research by DaDalt, Gay & Nam (2002) indicates that by using derivatives for hedging, managers are able to reduce macroeconomic shocks to earning, thus leading to lower earnings volatility, which is a common proxy for firm risk. Moreover, findings of Barton (2001) suggest that derivative users exhibit less risky cash flows than non-users, suggesting.

However, the derivatives activities of banks have received limited attention in the literature, so the motivations behind it still require extensive investigation. In their paper, Shiu & Moles analyze the Taiwanese banks in the period 1998-2005 using a probit model to test a range of potential motivations, which bring a range of interesting conclusion. The most important one for this paper is risk management being one of the main reasons for using derivatives. However, they also find a positive correlation between firm size and derivatives use, which indicates that the economies of scale factor is also a crucial driver as bigger banks have appropriate resources to establish efficient hedging programs. Hedging with derivatives is also connected to the size of foreign operations, as banks with more overseas income are more likely mitigate risk using both currency and interest-related derivatives. This finding is interesting in the context of investigating Polish banks, as a large share of Polish banking system is held by foreign banks, which could indicate there is a strong incentive for using derivatives for hedging purposes. Finally, they also conclude that banks, for which interest-sensitive

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11 liabilities dominate interest-sensitive assets, use more derivatives, while banks with the reverse trend seem unaffected.

The literature surrounding derivatives usage by financial firms provides more mixed results, however. Research by Peek and Rosegren (1997) suggests that many of the large banks involved in the derivatives market are high-risk units while Edwards and Mishkin (1995) find that engaging into derivatives activities can lead banks to take excessive risks that can be destabilizing to the banking system. On the contrary, research by Venkatachalam (1996) and Hassan et al. (1994) indicates that derivatives usage is associated with decreasing risk.

Broccardo, Mazzuca & Yaldiz (2015) analyze the Italian banking system to test the extent and motivations for credit derivatives usage. Based on the existing literature, they identify two major drivers for credit derivatives: managing credit risk and increasing diversification of the portfolio. They utilize a probit regression of the use of credit derivatives on multiple factors that serve as proxies for various motivations, and also investigate whether the motivations changed as a result of the subprime crisis. Similar to Shiu & Moles, they find that banks using derivatives are generally larger than non-users, as these banks are able to achieve the economies of scale in utilizing the derivatives. Within their analysis period of 2005-2011, they find that around 90% of Italian banks make use of any form of financial derivatives. However, while it is difficult to isolate a single reason for derivatives use in majority of the banks, when a single reason can be isolated, the pure trading purpose dominates the pure hedging purpose. Looking purely at the credit derivatives, they find that around 11% of all banks within the country utilized CDs between 2008 and 2011. Moreover, there are significant statistical differences between users and non-users, with non-user banks showing higher levels of risks and higher propensity for hedging the credit derivatives users. These findings indicate that credit derivatives are more likely to be used for speculation and not hedging. While their results do not provide any evidence to confirm the hedging rationale for derivatives use, the authors note that with the implementation of Basel 3, credit derivatives could emerge as an important tool to manage portfolio risk, serving as an alternative to deleveraging activity.

Instefjord’s (2005) theoretical paper also focuses on credit derivatives and their impact on bank risk levels. In his analysis, he finds two different channels for credit derivatives to impact risk, with contradicting effects, so the overall effectiveness of derivatives depends on which effect dominates. The first channel offers risk reduction as the risk-sharing effect of credit derivatives can be applied in hedging. The second channel leads to increased risk as credit derivatives increase the banks’ appetite for risk, leading to more risk-taking, which can

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12 destabilize the banking system, if the effect grows too strong. Instefjord also argues that this relation should hold even when credit derivatives are used solely for hedging purposes.

Keffala (2015) investigates emerging countries in the subperiods 2003-2006 and 2007-2011, along with the whole period, to test the effect of different derivative instruments on stability under different economic conditions. He finds that, while forwards and swaps are not disruptive, futures and options lower bank stability in emerging countries and can thus contribute to financial crises. In their research of South Korean banks, Yang, et al. (2006), find that the derivative holdings of banks are negatively correlated with the two measures for risk they employ. This suggests that market participants view derivatives activities as attempts to decrease the banks’ exposures. They point out that derivatives help in managing risk by reducing the noise from exogenous factors, which leads to lower risk. The evidence they gather also emphasizes the importance of implementing proper hedge-accounting rules, as more complex derivative disclosures which are required by South Korean regulators provide useful information about the underlying risk of derivatives transactions. Finally they reference evidence from US that only risk transferring derivatives are unassociated with risk while other derivatives seem to increase systematic risk.

Using quarterly data of US commercial banks between 2001 and 2016, Ghosh (2017) investigates the impact of derivatives on bank-specific risk, both in the pre-crisis (2001-2008) and post-crisis (2009-2016) periods. He points out that this section of research into derivatives is lacking as most authors focus on effects on systemic risk This existing literature finds a lot of support for negative correlation of derivatives with systemic risk, but offers little insight into how derivatives affect the individual banks. Ghosh analyzes the impact of both total derivatives, as well as its main components, that is interest-rate, exchange-rate, credit and equity derivatives on the risk levels of banks, as well as profitability. He finds that total derivative holdings, as well as interest-rate and exchange-rate derivatives lead to reduced bank-specific risk, while the other components have no significant impact on risk. However, only interest-rate derivatives are found to have significant impact on return volatility, leading to less volatile returns. These findings only hold for the pre-crisis period however, as their significance weakens greatly in the post-crisis period. Moreover, in the post-crisis period, derivatives are found to decrease profits, with the exchange-rate derivatives driving the effect, likely as a result of volatility spikes for many currencies worldwide. According to Ghosh, this finding shows the need for better regulations in the US, in order to reduce the costs of engaging into derivatives trading and maintain their profitability for banks.

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13 Dai and Laponte (2010) test the relation between derivatives and asset risk for Canadian banks in the period 1997-2007. They find that the risk of Canadian banks was really low, and decreasing, coming up to the 2008 recession. They conclude that such level of risk cannot be associated with derivatives and find that derivatives did not have a significant impact on asset risk. They attribute the low risk levels to prudent and conservative banking practices employed by Canadian banks and argue that the main foundation of a healthy and stable banking system is limiting the risk exposures in the first place, rather than hedging those risks.

Majority of the research focuses on the relation between risk and derivatives using only a single measure of derivative positions of banks, namely the notional value outstanding. International regulators are moving away from this measure as, despite the ease of reporting, it is not the optimal method to convey the information about the risk involved in the use of derivatives. Namely, notional amounts often fail to reflect the actual risk involved in a derivative transaction, thus providing limited informational content. Regulator are now moving towards the use of fair value estimates, which take into account all cash flows associated with the derivative, both present and future, and thus provide a lot more insight into the risks involved. However, most of the regulation is still relatively new, especially outside of United States which mean the fair value estimates are difficult to obtain. As a result, there is very limited research on how efficient the fair value estimates of derivatives are at explaining the variation in bank risk levels and whether they truly offer the risk reduction that is implied in theoretical channels.

3. Data and Methodology

3.1 Dataset preparation

The banking sector in the United States is highly regulated and strict requirements exist for reporting both on- and off-balance sheet items. Alongside reporting the notional amounts of their derivatives portfolio, SFAS 107 and 119 require banks to report the fair values of derivative positions, as well as whether they represent an asset or a liability and the purpose for which they are held: trading, hedging or other. Moreover, it requires banks to provide disaggregate data for each type of derivatives. This data is stored by the Federal Reserve System alongside other information, including balance sheets and income statements. All data is reported to FRS quarterly. The data for my research is obtained from the Bank Regulatory database of Wharton Research Data Services, which collects the data for all banks regulated by the Federal Reserve System from Federal Reserve Bank of Chicago. The sample period for my

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14 tests ranges from Q1 2001 to Q4 2013, so 52 quarters. I discard banks with total assets lower than $15 billion, as I aim to focus my research on large banks, whose improper risk management could lead to significantly increased systemic risk. Moreover, I drop observations with missing data. Finally, as I am only interested in banks using derivatives, I eliminate non-user banks which report 0 as fair value estimates in all 4 categories of derivatives. After these actions, the remaining dataset contains 3,042 observations for 130 banks.

3.2 Empirical model

In my research I utilize a model inspired by Ghosh (2017), who investigates the effects of notional amounts of derivatives on bank risk. I decided to adopt a model that was already utilized in existing literature as I want to see how the results using fair value data correspond to results obtained using notional amounts of derivatives, to see if the concerns from managers are reasonable and if the change of reporting method help with identification of risk associated in derivative transactions. As such, I will be using the following model:

𝑅_𝑖,𝑡 = 𝛽₀+ 𝛽₁𝐷𝐸𝑅_𝑖.𝑡+ ∑ 𝛽_𝜅𝑋_𝑖.𝑡 𝜅 𝑖=2 + ∑ 𝛿_𝑡 𝑡 𝑌𝑅_𝑡+ 𝜀_𝑖,𝑡

In his research Ghosh (2017) regresses the risk on a single derivative measure, 𝐷𝐸𝑅_𝑖.𝑡,

representing the banks’ position in either total derivatives or one of the derivative categories, resulting in 5 regressions for each dependent variable. This allows to precisely study the effect of the particular type of derivative on bank risk. A concern with the model, identified by Ghosh himself, is the potential endogeneity between the dependent variable and the derivative positions since increase in risk is likely to lead to increase in hedging and thus higher derivative positions. In order to eliminate the endogeneity issue, similarly to Ghosh, I use lagged values of all regressors, moving them back by one quarter, so that the model takes the following form:

𝑅𝑖,𝑡 = 𝛽0+ 𝛽1𝐷𝐸𝑅𝑖.𝑡−1+ ∑ 𝛽𝜅𝑋𝑖.𝑡 𝜅 𝑖=2 + ∑ 𝛿𝑡 𝑡 𝑌𝑅𝑡+ 𝜀𝑖,𝑡

In this model, 𝑅_𝑖,𝑡 is the dependent variable which represents risk for bank i in quarter

t, as measured by the Z-score values. The Z-score is a measure of insolvency risk based on the

balance sheet that indicates how much protection the banks has against shocks to earnings, where larger values indicate lower risk. The Z-score is calculate via the following formula:

𝑍 − 𝑠𝑐𝑜𝑟𝑒𝑖,𝑡 = [𝑅𝑂𝐴𝑖.𝑡+ (

𝐸𝑞𝑢𝑖𝑡𝑦

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𝑅𝑂𝐴_𝑖.𝑡 is the return on assets represented by the ratio of net income to average assets, and

𝜎(𝑅𝑂𝐴)_𝑖,𝑡 is the four-quarter moving standard deviation.

The introduction of fair value reporting for derivatives by SFAS 107 was widely opposed by bank managers and executives as it created numerous potential issues with the way banks reported their earnings and risk management. Besides making hedge accounting much more difficult to achieve as the hedges reported under fair value seemed less efficient than notional values, the requirement to report fair values meant that some methods of hedging would lead to banks’ earning patterns displaying much more volatility than they used to, potentially raising concerns from investors. In order to verify this, I will perform a secondary

regression which uses 𝜎(𝑅𝑂𝐴)_𝑖,𝑡 as the dependent variable as earnings volatility is also a

commonly used measure of risk. The expectations for this regression is that fair values of

derivatives should be positively correlated with 𝜎(𝑅𝑂𝐴)_𝑖,𝑡.

The variable 𝐷𝐸𝑅𝑖.𝑡 represents the net fair value position of a specific category of

derivative security as a share of its total assets, so dependent on the regression, total derivatives, interest rate derivatives, foreign exchange derivatives, equity derivatives and commodity and other derivatives. As derivatives should reduce the risk levels of bank, the expected coefficient of these variables is positive.

The vector 𝑋𝑖.𝑡 contains several variables used as controls in the regression. As banks in

the sample range from $150 million to $2 trillion in assets, the logarithmic assets and squared logarithmic assets are included to control for differences across class sizes such as economies of scale or utilization of different techniques to manage risks, alongside non-linear effects captured by the squared logarithm. The degree of leverage reflects the levels of risk a company faces, with more leveraged banks being riskier, so the equity-to-assets ratio is included to control for the extra risks more leveraged companies take on. Since lending is one of the primary activities of banks and a dominant source of risk, loan specialization and the credit risk borne as a result of banks’ lending activity are important factors that need to be accounted for in the regression, so a loan-to-assets ratio is included. This ratio can be interpreted twofold, as higher ratio might indicate a higher risk of default due to more exposure, however, it can also hint at effective management and reduction of the risk associated with these loans, thus allowing banks to accommodate more lending in their activities. To complement this control variable, net charge-off rate, that is the difference between loan charge-offs and loan recoveries, is included and serves as a measure of banks’ loan performance.

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16 One of the most common and ground-level methods of risk reduction is through the diversification of bank activities between interest and non-interest income. While the upfront expectation is that diversification lowers risk, Stiroh and Rumble (2006), find that the effect of diversification on risk is often ambiguous. While spreading their business over a multitude of services and activities can reduce banks’ risks, in the search for diversification these banks can enter into lines of business in which they lack expertise or which are still a novelty and are thus not understood well by the market yet. The increased exposure resulting from the volatility of these new services can often more than offset the benefits of diversification. Diversification is measured as one minus the sum of the squares of the share of non-interest and net interest incomes. The remaining control variable are deposits-to-assets ratio, which measures liability concentration and real GDP growth, which controls for the performance of the overall economy. On the following page, Table 1 presents descriptive statistics for all the variables in the dataset. Looking at the summary statistics, we can see that the interest rate derivatives are the biggest category of derivatives by a large margin, on average making up 83.5% of banks derivatives holding. The second largest category are the exchange rate derivatives, which constitute 13.5% of mean total derivatives. Commodity and equity derivatives both form around 2% of total derivatives, thus being much less significant that the other 2 categories. The average bank size in the sample is $129 billion, which is quite significant, however the median equals only around $47 billion, showing that there is a large spike in size at the top. The banks on average are very heavily leveraged, as the average equity-to-assets ratio is only 11.3% and the deposits-to-assets ratio average 66.2%. The banks also prove to be quite well diversified as the average diversification is 0.372 out of the maximum 0.5 and more than 75% have a diversification index of 0.3 or higher.

To reinforce the regressions and results, bank fixed effects are included to control for

cross-sectional differences and year dummies, 𝑌𝑅𝑡, account for regulatory changes in the US

banking sector over the years. Finally, the standard errors are clustered at bank level to eliminate potential autocorrelation issues.

Initial regression will be run using 𝑍 − 𝑠𝑐𝑜𝑟𝑒_𝑖,𝑡 as the dependent variable. Separate regressions

will be run for the total position in derivatives and for each of the categories of derivatives reported as fair value estimates. Additionally, as bank managers argue that fair values might increase the earnings volatility that they report, a secondary regression will be performed to test

this. In order to do this, the dependent variable used will be 𝜎(𝑅𝑂𝐴)𝑖,𝑡, which is also a common

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for the results. In the regressions using 𝑍 − 𝑠𝑐𝑜𝑟𝑒_𝑖,𝑡, the coefficients of all categories of

derivatives are expected to be positive, so that derivatives reduce insolvency risk, in line with their theoretical risk reduction benefits. The reverse is expected in regressions utilizing

𝜎(𝑅𝑂𝐴)𝑖,𝑡 as the dependent variable, as according to the managers, fair values should increase

earnings volatility, thus resulting in expected positive coefficients, which indicate increased volatility and risk.

Table 1. Descriptive statistics of the sample

Variables Observations Meana _{Std. Dev.} _Min _Max

Total derivatives 3,042 178.017 1127.902 0 17,080.160

Interest rate derivatives 3,042 148.660 1033.147 0 15,734.800

Foreign exchange

derivative 3,042 23.797 103.229 0 1,406.858

Equity derivatives 3,042 3.066 11.744 0 233.983

Commodity and other

derivatives 3,042 2.494 10.246 0 288.053 Z-score 3,042 40.814 69.488 1.154 2019.502 Risk-adjusted ROA 3,042 1.831% 1.692 -22.535% 39.172% ROA volatility 3,042 0.005 0.005 0.000 0.110 Log(Assets) 3,042 10.948 1.074 9.617 14.504 Log(Assets)^2 3,042 121.016 24.917 92.495 210.354 Loans-to-Assets 3,042 0.604 0.185 0.001 0.976 Deposits-to-Assets 3,042 0.662 0.146 0.008 0.946 Equity-to-Assets 3,042 0.113 0.046 0.036 0.528 Diversification 3,042 0.372 0.101 0 0.5

Net Charge-Off Rate 3,042 0.008 0.015 -0.008 0.249

Real GDP growth 3,042 1.745 1.784 -4.1 4.4

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18 This procedure will also be replicated on two sub-samples of the data set to analyze how the financial crisis of 2008 affected the banking industry and the riskiness of banks. The first sub-sample is the pre-crisis period and ranges from Q1 2001 to Q4 2007 and the second subsample is the post-crisis period ranging from Q1 2008 to Q4 2013. The expectation is that derivatives will be less efficient at reducing risk in the post-crisis period than in the post-crisis

period, so that for 𝑍 − 𝑠𝑐𝑜𝑟𝑒𝑖,𝑡 𝛽𝑖,𝑝𝑟𝑒−𝑐𝑟𝑖𝑠𝑖𝑠 > 𝛽𝑖,𝑝𝑜𝑠𝑡−𝑐𝑟𝑖𝑠𝑖𝑠. For 𝜎(𝑅𝑂𝐴)𝑖,𝑡, using the same

intuition, the lower efficiency of hedging in the post-crisis period should result in higher

earnings volatility than in the pre-crisis period, so the expectation is that 𝛽_{𝑖,𝑝𝑟𝑒−𝑐𝑟𝑖𝑠𝑖𝑠} <

𝛽_{𝑖,𝑝𝑜𝑠𝑡−𝑐𝑟𝑖𝑠𝑖𝑠.}, that is using fair value estimates of derivatives will increase the volatility of returns even more in the post-crisis period than in the pre-crisis period.

Finally, an analysis of the risk-return trade-off will be conducted to see whether the changes in risk levels caused by derivatives are part of the trade-off or whether these financial instruments offer additional benefits in risk management. In order to achieve this, risk-adjusted returns on assets will be used as the dependent variable and regressed on the fair value estimates of derivatives.

3.3 Hypotheses development

Based on the expectations set out in the previous section, the following hypotheses were formed:

Hypothesis 1:

H0: Derivatives positions for aggregate and separate categories reduce risk levels of banks.

H1: Derivatives positions for aggregate value and separate categories increase risk levels of US

banks or offer no benefits.

Hypothesis 2:

H0: The effect of derivatives positions does not differ significantly between the periods.

H1: The effect of derivatives positions on risk levels is higher in the pre-crisis period than in the

post-crisis period.

Hypothesis 3:

H0: The effect of derivatives on profits does not differ significantly between the periods.

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19

4. Results

4.1 Bank risk results

The results for regressions with 𝑍 − 𝑠𝑐𝑜𝑟𝑒_𝑖,𝑡 as the dependent variable are presented in Table 2

below. The coefficient for total derivatives is positive, meaning that is should decrease insolvency risk, and it is statistically significant at the 10% level. The sign of the coefficient is thus consistent with the expectation that derivatives reduce risk. The biggest category of derivatives, the interest rate derivatives, is unsurprisingly found to have a positive sign, suggesting risk reduction benefits coming from their usage, which is also significant at the 10% level. The significance of this category is the primary driver for the significance of total derivatives as the vast majority of derivatives used are interest rate derivatives. This suggests that US banks have utilized interest rate derivatives efficiently to reduce their risks, bolstering their resistance to unforeseen shocks to earnings. This is consistent with the findings of Ghosh (20017) who used notional amounts of derivatives reported by banks, however, the estimated coefficients in my regression are slightly lower. This might indicate that the notional amounts underestimate the risk involved in transactions involving interest rate derivatives. The result for exchange rate derivatives is quite surprising. While it is found statistically insignificant, the estimated coefficient is negative, which would indicate that exchange rate derivatives are expected to increase insolvency of banks. Multiple interpretation of such result come to mind. On one hand, it might mean that American banks are not capable of utilizing these derivatives efficiently in hedging, taking on greater risk instead of reducing it. On the other hand, it is possible that the notional amounts that were used to report derivative positions for so long heavily misinterpreted the risk involved in foreign exchange transactions, which could occur as a result of the complexity of international markets, especially around the 2008 crisis. Finally, the simplest explanation could be that American banks do not engage into many foreign currency transactions and thus do not need to hedge against them, so that majority of their foreign exchange derivatives are used for speculation, which bring in more risk rather than shed it. The two minor categories of derivatives, equity and commodity, are found insignificant even at the 10% level, and while the estimated coefficient for Equity derivatives is positive, the coefficient for Commodity derivatives is negative, suggesting that similar to exchange derivatives they would increase insolvency risk rather than reduce it.

Looking at the control variables presents us with a few surprising results, that contradict expectations. The primary surprise is that the coefficient for firm size is positive and significant,

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20 which suggests that bigger banks are inherently less risky. This is incredibly surprising as typically larger companies face significantly more risk than smaller ones yet in this case that trend is completely reversed. The differences in size across the sample are substantial as the smallest bank is about 130 times smaller than the biggest. This might imply that the biggest banks, dues to more funds available, are able to implement much higher quality of risk management programs which allows them to reduce the risk through a variety of tools, such as derivatives or securitization. However, squared firm size has a negative coefficient, which implies that the risk reducing effect of bank size decreases in strength the bigger the banks become. Equity-to-assets ratio is significant at 1% level and has a positive coefficient. This result is not surprising as a higher ratio implies that a bank is less leveraged and higher levels of leverage are associated with big increases in risk. This results is consistent with the findings obtained using notional amounts of derivatives instead, however, the coefficient is about two times larger, suggesting that leverage contributes to risk more significantly than previous evidence implied. Loans-to-assets ratio is the final control variable found to be significant, at 10% level, and its estimated coefficients are negative. As I have explained previously, higher loans ratio implies that banks face more exposure in their activities and thus experience increased risk, which they might not be able to offset with higher expertise in the area. Moreover, higher reliance on loans means a bigger part of the bank’s income coming from one source, thus limiting the potential for diversification, which could help reduce risks. Similarly to leverage ratio, the estimated coefficient is higher than that obtained in research utilizing notional amounts, implying that the effect on insolvency of loan exposure is higher than anticipated. These results might imply that the notional amounts of derivatives capture the effects on risk associated with these two categories, while the fair values which better reflect the underlying risk allow these effects to be traced to their origin, or it might be the case that the fair values are flawed and fail to reflect the risk that thus gets captured by the controls. The coefficients for dividends and GDP growth are positive, consistent with expectations, however, they are not significant. The deposits-to-asset ratio and net loan charge-offs are both also insignificant, however the estimated coefficients are quite surprising. Higher loan charge-offs would imply higher Z-scores and thus less insolvency risk, which contradicts the expectations that lower quality loans would lead to more variable income and thus higher risk of failure. Deposits-to-assets ratio is negatively correlated with Z-score suggesting that higher reliance on deposits as the funding method increases the risk banks face.

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21 T ab le 2. R esu lts fo r r eg re ssi on s of Z -sc or e C omm odit y De riva ti ve s (5) -0.080 _(0.16 3) 114.400** (55 .150) -4.301** (2.17 0) 251.200*** (55.7 30) -52.130* (27.1 2) -1.8710 _(21.9 20) 17.060 _(26.1 20) 42.140 _(89.6 30) 0.266 _(4.10 5) 2,880 Robust stand ar d err ors clust er ed at bank lev el re port ed in brac ke ts, * sig nif icant at 10% lev el, ** signi fi cant at 5% lev el, *** signi fi cant at 1% lev el Equit y De riva ti ve s (4) _0.227 (0.31 8) 119.300** (54.6 80) -4.534** (2.15 2) 252.000*** (56.1 10) -51.710* (27.2 90) -1.229 _(22.0 10) 17.760 _(26.1 60) 34.390 (87.9 8) 0.274 _(4.10 4) 2,880 Exc ha nge D eriva ti ve s (3) -0.002 _(0.01 7) 116.9 00** (56.6 50) -4.420* (2.25 2) 251.000*** (55.9 40) -52.440* (27.1 00) -1.956 _(22.0 20) 17.630 _(26.1 50) 40.230 _(89.0 30) 0.276 _(4.10 7) 2,880 Inte re st De riva ti ve s (2) 0.005* (0.00 2) 121.200** (56.1 10) -4.604** (2.21 9) 249.300*** (55.8 60) -51.860* (27.0 70) -1.281 _(21.8 70) 17.610 _(26.1 30) 39.250 _(88.7 60) 0.216 _(4.1 13) 2,880 Total De riva ti ve s (1) 0.004* (0.00 2) 120.600** (56.0 60) -4.580** (2.22 17) 249.400*** (55.8 50) -51.860* (27.0 80) -1.244 _(21.8 90) 17.670 _(26.1 40) 38.930 _(88.8 60) 0.220 _(4.1 13) 2,880 De riva ti ve s/Ass ets t-1 Log( Asse ts) t-1 Log( Asse ts) 2 t-1 C apit al/ Asse ts t-1 Loa ns/Assets t-1 De posi ts/ Asse ts t-1 Dive rsific ati on t-1 Ne t C ha rge -of fs t-1 R ea l GDP grow th t-1 N

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22

4.2 Earnings volatility results

Table 3 presents the results for regressions using ROA volatility as the dependent variable. The resulting coefficients for the derivative categories present a similar picture as in the previous chapter. Total derivatives are negatively correlated with ROA volatility, meaning that derivatives reduce risk, and the coefficient is significant at the 1% level. This is consistent with theory as derivatives enable banks to hedge their risk and thus ensure a more stable income. Similar findings are observed for interest rate derivatives, as the coefficient is once again negative and significant at 1% level, implying risk reduction benefits come from usage of interest rate derivatives. As this is the dominant category of derivatives for majority of the banks, the significance of this results drives the result for total derivatives. The other 3 categories of derivatives provide insignificant coefficients. The estimated coefficients for commodity and equity derivatives are negative, consistent with expectation that derivatives reduce risk. However, the coefficient for exchange rate derivatives is positive, implying that this type of derivatives increases earnings volatility and thus risk. Several interpretations of this result are possible. First of those is that banks might be using currency derivatives inefficiently, leading to higher risk levels instead of reducing them. Second explanation suggests that US banks conduct relatively few foreign transactions, and thus their positions in this category are mostly speculative, focused on betting on the currency movements. The third rationale for this result is that after the 2008 crisis, many currencies worldwide experienced spikes in their volatilities, turning attempts of hedging those risk into an enormous challenge, that banks could not adapt to immediately. I will investigate whether this holds true later, when I analyze the differences between pre- and post-crisis periods.

In contrast to the results for Z-score, only two control variables maintain significance this time. Loans-to-assets ratio is significant at 10% level and has a positive coefficient, implying that more loan exposure drives up the earnings volatility. This is consistent with theory as heavier reliance on loans means that banks face more exposure and thus more chances for these loans to fail. Moreover, heavy focus on as single source of income reduces the potential for diversification, which should decrease variance in earnings. Real GDP growth is significant at the 5% level and has a negative coefficient, that is consistent with theory, as high positive GDP growth should decrease risk by allowing banks more opportunities to profit from while facing lower risk. The other control variables provide insignificant coefficients, however the estimates are consistent with theory expect for diversification, which has a positive coefficient that suggests it would increase the risk banks are exposed to.

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23 T ab le 3. R esu lts fo r r eg re ssi on s of R OA volatil ity C omm odit y De riva ti ve s (5) -0.00000058 _(0.00 000966) 0.00279 _(0.00 316) -0.000154 (0.00 140) -0.00493 _(0.00 452) 0.00899* (0.00 526) -0.00420 _(0.00 458) 0.000744 (0.00 285) 0.031 1 (0.03 29) -0.000375** (0.00 0172) 2,880 Robust stand ar d err ors clust er ed at bank lev el re port ed in brac ke ts, * sig nif icant at 10% lev el, ** signi fi cant at 5% lev el, *** signi fi cant at 1% lev el Equit y De riva ti ve s (4) -0.00001 72 (0.00 001 91 ) 0.00263 _(0.00 309) -0.000146 _(0.00 0136) -0.00501 _(0.00 454) 0.00893* (0.00 526) -0.00425 _(0.00 457) 0.000739 (0.00 285) 0.0315 _(0.03 27) -0.000375** (0.00 0172) 2,880 Exc ha nge D eriva ti ve s (3) 0.00000156 _(0.00 000250) 0.0 0280 (0.00 321) -0.000154 _(0.00 0137) -0.00499 _(0.00 457) 0.00901* (0.00 529) -0.00416 _(0.00 452) 0.000756 (0.00 284) 0.0310 _(0.03 27) -0.000377** (0.00 0175) 2,880 Inte re st De riva ti ve s (2) -0.000000808*** (0.00 0000301) 0.00214 _(0.00 299) -0.000126 _(0.00 0131) -0.00468 _(0.00 451) 0.00890* (0.00 523) -0.00430 _(0.00 458) 0.000753 (0.00 285) 0.0312 _(0.03 29) -0.000366** (0.00 0171) 2,880 Total De riva ti ve s (1) -0.000000643*** (0.00 0000224) 0.00225 _(0.00 300) -0.000131 _(0.00 0132) -0.00471 _(0.00 453) 0.00891* (0.00 524) -0 .00430 (0.00 457) 0.000744 (0.00 285) 0.0313 _(0.03 28) -0.000367** (0.00 0172 ) 2,880 De riva ti ve s/Ass ets t-1 Log( Asse ts) t-1 Log( Asse ts) 2 t-1 C apit al/ Asse ts t-1 Loa ns/Assets t-1 De posi ts/ Asse ts t-1 Dive rsific ati on t-1 Ne t C ha rge -of fs t-1 R ea l GDP grow th t-1 N

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24

4.3 Pre- and post-crisis risk results

The crisis in 2008 dramatically changed the economic conditions in the US and created enormous uncertainty, which is very concerning for the efficiency of derivatives in both hedging and speculation. It is thus worthwhile to investigate how the 2008 recession impacted the relation between risk and the use of derivatives.

Table 4 present results of regressions with Z-score as a dependent variable in the pre-crisis period 2001-2007. Looking at the results, we can see that the coefficient for Total Derivatives is much more significant in the pre-crisis period than across the whole sample, remaining significant even at 1% level. The coefficient is once again positive, which means in the pre-crisis period, the derivatives contribute to reducing insolvency risks. Similar findings are seen when we look at the main category of derivatives, the interest rate ones, which also experience increased significance up to 1% level and show a positive correlation with Z-score, implying risk reducing benefits of interest rate derivative before the financial crisis. The size of both coefficients has also significantly increased, implying that these derivatives were used more efficiently in the pre-crisis period to manage the risks that banks faced. The other categories of derivatives show more significant differences when compared to the full sample. Looking at the exchange rate derivatives, we see that while the coefficient is statistically insignificant, contrary to the full sample analysis, the sign of it is positive, implying that in the pre-period risks, exchange rate derivatives were used to manage risk in an efficient manner. The equity derivatives in the pre-crisis period remain insignificant, however, their coefficient also changes, showing a negative sign this time, which might suggest that these derivatives were used primarily to speculate in the pre-crisis period. The commodity derivatives do not see any significant changes from the full-sample analysis.

The results for the post-crisis period can be seen in Table 5. The total derivatives are not significantly related to risk as the coefficient for the post-crisis period is much lower than that for full sample. With the increased volatility following the 2008 crisis, successful hedging with derivatives must have become a much greater challenge due to the unpredictability of the market, which means banks had to make substantial adjustments to achieve pre-crisis efficiency. It is likely these adjustments have not yet been completed and it is impossible to tell how much time passed before banks realized the need for such adjustments. Once again, as interest rate derivatives make up an enormous part of all derivatives and thus drive the result for total derivatives, a similar trend can be observed in results for this category, as the coefficient

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25 decreases substantially so the significance of the relation to risk wanes. Similarly to the pre-crisis period, the coefficient for exchange rate derivatives is insignificant and positives, which makes the result for the full sample quite peculiar, as trends must emerge across the whole period that alter the coefficient to become negative. The equity and commodity derivatives are both insignificant and show positive coefficients, which is new for the commodity derivatives. The change is however reasonable as the negative coefficient for the pre-crisis period is stronger than that for the full sample, so the post-crisis change offsets some of the pre-crisis effect. Despite the insignificance of exchanger rate, equity and commodity derivatives in both the pre- and post-crisis period, their t-statistics are still much higher before 2008 than they are after the crisis, which implies that as the recession introduced great uncertainty into the economy, using any category of derivatives became much more challenging when hedging risks is concerned. The only control variable that remains significant is the leverage ratio as the magnitude of its effect does not change significantly in statistical sense, as lower levels of leverage still increase Z-score significantly. The coefficient is much higher for the post-crisis period however, which implies that as the crisis developed, low levels of leverage became even more crucial for maintaining insolvency risks low. In the pre-crisis period, the net charge-off rate also gains significance and it shows an even higher positive coefficient than across the full sample, which becomes even more peculiar as loan charge-offs should not help to reduce insolvency risk while they decrease the potential profits of a company and indicate lower loan quality. The positive coefficient of firm size across the full sample is dominated by the post-crisis results, indicating that under unfavorable economic conditions, the extra capital that these banks have access to allows them to manage the risks introduced by an economic downturn with increased efficiency compared to banks with less resources to spare. In the pre-crisis period for total and interest rate derivatives, the coefficient for firm size becomes negative, consistent with the theory that larger banks are inherently more risky. While regressions using the other categories still show positive coefficients, total and interest rate derivatives show most significance as these derivatives are the most popular among banks, so it can be assumed that the theory holds true in the pre-crisis period, while the turbulent circumstances of the crisis invalidate it as the extra capital helps prevent bankruptcy. The loans exposure loses significance in both subperiods but it remains negative, however, the coefficient is closer to zero for the pre-crisis period which might imply that before the crisis, the business expertise and specialization were more able to offset the extra exposure from taking on more loans. The remaining control variables remain insignificant across both subperiods.

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26 Tables 6 and 7 show results with earnings volatility as the dependent variable. Table 6 presents pre-crisis results, while table 7 contains post-crisis results. Surprisingly, while total and interest rate derivatives maintain significance in only one period, this time it is the post-crisis period, as the significance in the years 2001-2007 wanes. Throughout both periods, the coefficients are negative meaning that interest rate derivatives decrease earning volatility. In the turbulent period, both are significant at the 1% level and show stronger coefficients than in the pre-crisis period, which implies that the risk reduction benefit is greater during and after the recession than before it, which contradicts the expectations. The existing research utilizing notional amounts of derivatives shows that before the crisis, derivatives reduce earnings volatility. Taking this into account, the pre-crisis insignificance of fair value positions might serve as a confirmation of the concerns managers had surrounding the new method of reporting. While fair value estimates do not directly increase earnings volatility, they fail to provide the same risk reduction that notional amounts did, which means that the volatility reported under the new method would indeed be higher than previously. The significance of the post-crisis results might stem from the erratic nature of economic downturn that has especially strong impact on instruments such as derivatives. The coefficient for exchange derivatives gains significance in the pre-crisis period, and it becomes negative meaning that before 2008, banks were able to successfully hedge currency risks using derivatives. In the post-crisis period, the coefficient remains insignificant and positive. In the aftermath of the crisis, the volatility of many currencies increased significantly, which likely made the currency derivatives inefficient and led to increased earnings volatility. The equity and commodity derivatives remain insignificant throughout and their negative coefficients indicate that these types of derivatives would most likely lead to risk reduction.

Firm size seems to have a reverse effect on earnings volatility than on insolvency risk. Bigger firms seem to experience less volatility in earnings before the crisis, while after the crisis firm size is positively correlated with earnings uncertainty. Loan charge-offs also seem to lead to risk reduction in the pre-crisis period, while as the crisis began, the coefficient becomes positive again, indicating higher risk as the quality of loans given out decreases. The coefficient for GDP growth remains significant only for the post-crisis period, however, it reduces earnings volatility in both subperiods, similar to the full sample.

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27 T ab le 4. R esu lts fo r Z -sc or e in the per iod 2001 -2007 C omm odit y De riva ti ve s (5) -0.1 19 (0.39 6) 9.853 (30.1 30) -0.357 _(1.28 5) 252.600*** (58.7 50) -21.290 _(12.9 80) -0.935 _(12.0 20) -38.00 _(30.0 20) 90.420* (45.5 3) -0.927 _(1.095) 1,558 Robust stand ar d err ors clust er ed at bank lev el re port ed in brac ke ts, * sig nif icant at 10% lev el, ** signi fi cant at 5% lev el, *** signi fi cant at 1% lev el Equit y De riva ti ve s (4) -0.224 _(0.40 5) 6.223 _(28.9 10) -0.187 _(1.23 9) 248.900*** (59.2 90) -22.720* (13.1 30) -2.680 _(12.8 80) -37.930 _(30.1 10) 94.930* (48.6 00) -0.900 _(1.07 2) 1,558 Exc ha nge D eriva ti ve s (3) 0.0188 _(0.05 32) 11.570 _(25.1 50) -0.442 _(1.04 7) 253.700*** (58.7 9) -21.500 _(12.9 70) -0.955 ₍₁1.940) _-38.170 _(30.2 30) 87.600* (45.0 20) -0.9 53 (1.05 3) 1,558 Inte re st De riva ti ve s (2) 0.0357*** (0.01 15) -6.649 _(29.8 50) 0.401 _(1.28 7) 258.400*** (58.7 40) -19.260 _(13.5 90) 2.075 (12.2 00) -39.470 _(29.9 40) 85.410* (45.8 30) -1.142 _(1.16 0) 1,558 Total De riva ti ve s (1) 0.0302*** (0.00 840) -5.070 _(28.570) 0.326 _(1.22 5) 259.100*** (58.7 20) -19.360 _(13.5 00) 2.005 _(12.0 5) -39.170 _(29.9 90) 82.740* (43.2 70) -1.154 _(1.14 7) 1,558 De riva ti ve s/Ass ets t-1 Log( Asse ts) t-1 Log( Asse ts) 2 t-1 C apit al/ Asse ts t-1 Loa ns/Assets t-1 De posi ts/ Asse ts t-1 Dive rsific ati on t-1 Ne t C ha rge -of fs t-1 R ea l GDP grow th t-1 N

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28 T ab le 5. R esu lts fo r Z -sc or e in the per iod 2008 -2013 C omm odit y De riva ti ve s (5) 0.0184 _(0.06 47) 127.900 _(129. 800) -5.939 _(5.89 1) 345.200** (160. 000) -40.320 _(40.7 20) 4.464 (24.1 20) -40.820 _(58.9 70) 117.800 ₍₁₄₄ .300) 1.080 _(6.62 9) 1,322 Robust stand ar d err ors clust er ed at bank lev el re port ed in brac ke ts, * sig nif icant at 10% lev el, ** signi fi cant at 5% lev el, *** signi fi cant at 1% lev el Equit y De riva ti ve s (4) _0.665 (0.53 4) 123.600 _(125. 900) -5.767 _(5.71 4) 339. 700** (1.61 .700) -42.490 _(40.8 70) 2.864 _(24.3 90) -36.530 _(59.8 10) 119.700 _(145. 000) 1.1 18 (6.67 1) 1,322 Exc ha nge D eriva ti ve s (3) 0.00155 (0.02 17) 126.700 _(127. 800) -5.888 _(5.81 2) 344.400** (160. 000) -40.400 _(40.8 00) 4.434 _(23.8 10) -41.040 _(59.2 10) 117. 900 (144. 300) 1.073 _(6.63 4) 1,322 Inte re st De riva ti ve s (2) 0.000610 (0.00 209) 127.000 _(127. 600) -5.899 _(5.80 2) 344.200** (160. 700) -40.360 _(40.6 80) 4.415 (24.0 50) -41.130 _(59.2 50) 118.000 _(144. 100) 1.065 _(6.63 7) 1,322 Total De riva ti ve s (1) 0.000688 (0.00 197) 127.000 _(127. 600) -5.899 _(5.80 3) 343.900** (160. 900) -40.370 _(40.6 70) 4.481 _(24.0 40) -41.040 _(59.3 80) 117.900 _(144. 100) 1.064 _(6.63 7) 1,322 De riva ti ve s/Ass ets t-1 Log( Asse ts) t-1 Log( Asse ts) 2 t-1 C apit al/ Asse ts t-1 Loa ns/Assets t-1 De posi ts/ Asse ts t-1 Dive rsific ati on t-1 Ne t C ha rge -of fs t-1 R ea l GDP grow th t-1 N

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29 T ab le 6. R esu lts fo r ROA volatil ity in the per iod 2001 -2007 C omm odit y De riva ti ve s (5) -0.00000820 _(0.00 000913) -0.00185 _(0.00 236) 0.0000379 _(0.00 00976) -0.00332 _(0.00 394) 0.00248 _(0.00 23 3) 0.00179 _(0.00 203) 0.00363* (0.00 193) -0.00421 (0.01 11) -0.000102 _(0.00 00902) 1,558 Robust stand ar d err ors clust er ed at bank lev el re port ed in brac ke ts, * sig nif icant at 10% lev el, ** signi fi cant at 5% lev el, *** signi fi cant at 1% lev el Equit y De riva tives (4) -0.0000109 _(0.00 00154) -0.00194 _(0.00 232) 0.0000424 _(0.00 00996) -0.00348 _(0.00 387) 0.00240 _(0.00 229) 0.00170 _(0.00 203) 0.00362* (0.00 194) -0.00402 (0.01 11) -0.000101 _(0.00 00901) 1,558 Exc ha nge D eriva ti ve s (3) -0.00000993** (0.00 000482) -0.0004 00 (0.00 239) -0.0000297 _(0.00 00978) -0.00350 _(0.00 393) 0.00238 _(0.00 229) 0.00169 _(0.00 201) 0.00351* (0.00 193) -0.00367 (0.01 11) -0.0000887 _(0.00 00887) 1,558 Inte re st De riva ti ve s (2) -8.92*E -8 (0.00 00006) -0.00152 _(0.00 242) 0.0000226 (0.00 0103) -0.00328 _(0.00 400) 0.00245 _(0.00 235) 0.00177 _(0.00 205) 0.00361* (0.00 193) -0.00431 (0.01 10) -0.000102 _(0.00 0091 1) 1,558 Total De riva ti ve s (1) -0.000000452 _(0.00 0000513) -0.00129 _(0.00 241) 0.00001 19 (0.00 0101) -0.00335 _(0.00 399) 0.00242 _(0.00 234) 0.00163 _(0.00 205) 0.00361* (0.00 193) -0.00423 (0.01 10) -0.0000989 _(0.00 00908) 1,558 De riva ti ve s/Ass ets t-1 Log( Asse ts) t-1 Log( Asse ts) 2 t-1 C apit al/ Asse ts t-1 Loa ns/Assets t-1 De posi ts/ Asse ts t-1 Dive rsific ati on t-1 Ne t C ha rge -of fs t-1 R ea l GDP grow th t-1 N

The effect of fair value derivatives estimates on risk levels of US banks