Procyclicality of US Bank Leverage

Transcription

1 Procyclicality of US Bank Leverage Christian Laux and Thomas Rauter First Version: February 19, 2014 This Version: May 9, 2014 Abstract We provide empirical evidence on the prevalence and determinants of leverage procyclicality for US commercial and savings banks. We find that bank leverage is strongly procyclical even after controlling for a large set of economic and bank-specific determinants of leverage. Our findings do not suggest that marking-to-market is a main driver of procyclicality. Instead, our findings are consistent with banks using an expansion of their business to adjust their leverage and capital ratios towards their target levels, which gives rise to procyclicality. The drivers of leverage procyclicality differ for savings banks as well as commercial banks with more, respectively less, than 20% of their assets recognized at fair value. Understanding the determinants of procyclical bank leverage is important for the identification of possible problems and remedies that are as diverse as reporting, regulation, and management. JEL-Classification: E32, G20, G28, G32, M41 Keywords: Procyclicality, Leverage, Banks, Financial Crisis, Liquidity, Financial Regulation, Mark-to-Market WU (Vienna University of Economics and Business), Department of Finance, Accounting and Statistics, Vienna, Austria. Corresponding author: christian.laux@wu.ac.at VGSF (Vienna Graduate School of Finance) and WU (Vienna University of Economics and Business), Department of Finance, Accounting and Statistics, Vienna, Austria We thank Alois Geyer, Robert Kremslehner, Christian Leuz, Alex Mürmann, Florian Nagler and participants at the 2013 VGSF Conference for helpful comments and suggestions.

2 1 Introduction There is a large debate about the significance and origin of procyclical bank leverage among researchers and regulators (e.g., Plantin et al. (2008), Persaud (2008), BIS (2009) and IMF (2008)). Several possible reasons for procyclicality are provided in the theoretical literature, including, marking-to-market based financial reporting, collateralized financing and margin requirements, value-at-risk based bank management, and prudential regulation (e.g., Brunnermeier and Pedersen (2009), Adrian and Shin (2014) and Danielsson et al. (2012)). Understanding the determinants of procyclical bank leverage is important for the identification of possible problems and remedies that are as diverse as reporting, regulation, and management. We provide empirical evidence on the prevalence and determinants of leverage procyclicality for US commercial and savings banks, covering the period from Q to Q We follow Adrian and Shin (2010) and define procyclical leverage as a positive relation between changes in bank leverage ( Leverage) and changes in total assets ( Total Assets). That is, procyclicality arises if bank leverage increases/decreases when banks expand/contract their balance sheets. We find that bank leverage is strongly procyclical even after controlling for a large set of possible determinants of bank capital structure, including macroeconomic conditions (GDP growth and changes in VIX), the initial leverage, the market-to-book-ratio, and different regulatory capital measures (total regulatory capital ratio and changes in the average risk weight). We also include unrealized gains/losses on available-for-sale (AfS) securities, trading income, and realized gains from the sale of loans as well as AfS and heldto-maturity securities (HtM) to capture possible effects of accounting and profitability. The coefficients of our regression variables have the predicted signs and nearly all of 1

3 them are significant. However, successively including the control variables hardly changes procyclicality as measured by the level of association between Total Assets and Leverage. To investigate possible drivers of procyclicality we split our sample into three subgroups: savings banks, commercial banks with less than 20% of total assets measured at fair value (i.e., trading assets and AfS securities), and commercial banks with more than 20% of total assets measured at fair value. We find that procyclicality is higher for savings banks than for commercial banks (including those with more than 20% of total assets measured at fair value). As an alternative test, we split our sample based on the fraction of total assets measured at historical cost versus fair value and find that the measure of procyclicality for banks with more than 95% of total assets recognized at historical cost is not different from the measure of procyclicality for banks with more than 30% of total assets being recognized at fair value. The distribution of Total Assets is also similar for both types of banks. Therefore, our findings are not consistent with the idea that marking-to-market could be a main driver of procyclicality or that switching to historical cost accounting could reduce procyclicality. To understand the drivers of leverage procyclicality, we interact Total Assets with several market and firm characteristics. The coefficient of the interaction term with GDP growth is highly statistically significant, which confirms the intuition that procyclicality is strongly associated with the business cycle. We also find that procyclicality is stronger for institutions with low leverage and high regulatory capital ratios. This suggests that banks use an expansion of their business to also adjust their leverage and capital ratio towards their target levels, which gives rise to procyclicality. This finding is consistent with the observation that banks retain a high fraction of earnings (e.g., Berger et al. (2008)), which implies that adjustments to the optimal leverage and capital ratios are associated with increases in debt. Interestingly, we find that, when total assets decrease, the decrease in 2

4 leverage is higher if the bank s average risk weight increases. This suggests that banks sell liquid assets that have low risk weights to repay debt. We also investigate the role of accounting and profitability for procyclical leverage. The interaction of realized gains on loans with Total Assets is positive and highly statistically significant, but only when total assets increase, not when they decrease. Thus, it seems that banks that are active in the business of securitizing loans pursue an expansion strategy financed by debt, presumably to generate new loans to be securitized. The interaction terms of unrealized gains on AfS securities, realized gains on AfS & HtM securities, and trading income are not statistically significant. For savings banks, realized gains on loans and the market-to-book ratio are the only interaction terms with significant coefficients. The coefficient on the market-to-book ratio of equity suggests an interesting difference between savings banks and commercial banks in how they finance their assets when their market value is high. While commercial banks seem to raise equity when their market value increases, savings banks react more procyclically by increasing total assets and leverage. An interesting difference between the two types of commercial banks arises with respect to the role of regulation. If a bank s regulatory capital ratio is slack, the bank can increase its leverage without changing the average risk weights of its assets. In contrast, if the regulatory capital ratio is binding, an increase in leverage is only possible if the average risk weight of the assets decrease (Amel-Zadeh et al. (2013)). We find that for banks with less than 20% fair-value assets, procyclicality of leverage is higher if these banks have more regulatory slack. Moreover, a contraction of the balance sheet is associated with a higher reduction of leverage as average risk weights decrease. The latter finding is consistent with these banks selling liquid assets to repay debt. For banks with more than 20% fair-value assets, we find that regulatory capital slack has no significant impact on procyclicality. In- 3

5 stead, procyclicality is strongly associated with decreasing (increasing) average risk weights when total assets increase (decrease). Thus, the findings for commercial banks with more than 20% fair-value assets are consistent with the argument of Amel-Zadeh et al. (2013) that procyclicality is strongly linked to changes in the average risk weight so that changes in leverage do not impact the regulatory capital ratio. Although our distinguishing criterion is the fraction of fair-value assets, our evidence does not suggest that the results are driven by the differences in accounting. It is more plausible that the differences in accounting merely capture differences in the types of assets, including liquidity, risk, and risk weights, that these banks hold. In particular, commercial banks with more than 20% fair-value assets expand by investing in securities with low risk weights, while commercial banks with less than 20% fair-value assets have more loans on their balance sheet and expand their loan business. Also consistent with this interpretation is the positive coefficient of the interaction term of Total Assets with realized gains on loans, which is significant for commercial banks with less than 20% fair-value assets. Our research is motivated by Adrian and Shin (2010), who document a strong procyclical relation between Total Assets and Leverage for investment banks, but not for commercial banks. This finding likely reinforced the belief that marking-to-market could be a main driver of procyclicality since, though not the only difference, marking-to-market is prevalent for the former but not for the latter banks. However, Adrian and Shin (2010) used flow of funds data and, as both authors pointed out, it appears that the procyclical relationship gets lost in the flow of funds data (Adrian and Shin (2011), page 12). Our findings are consistent with Adrian and Shin (2011) and Greenlaw et al. (2008) who document a procyclical relation also for commercial banks. While Adrian and Shin (2011) look at all US commercial banks from Q to Q1-2010, Greenlaw et al. (2008) focus on the 5 largest institutions between 1988 and 2007 (also quarterly data). The focus of these 4

6 two papers is to explore the impact of procyclical bank leverage on aggregate liquidity (credit/funding conditions), economic growth and systemic risk. In constrast, the focus of our paper is to empirically identify possible determinants of leverage procyclicality on a bank-level and to distinguish between different business models. Our study is related to an independent and contemporaneous paper by Amel-Zadeh et al. (2013), who investigate whether fair-value accounting contributes to procyclical leverage of commercial banks. The authors develop a one-period model of commercial bank behavior in which they show that if a bank s regulatory capital constraint is binding, procyclicality can only arise if the average risk weight decreases (increases) upon balance sheet expansions (contractions). Amel-Zadeh et al. (2013) test their model empirically and include the change in average risk weight as a control variable when measuring procyclicality of banks (for Q Q4 2010). The change in average risk weight is highly statistically significant. Interestingly, when including this control variable, the coefficient on change in total assets becomes insignificant. Thus, the authors conclude that procyclicality is mainly an effect of differences in regulatory risk weights and changes in average risk weights when banks expand or reduce total assets. We include the change in average risk weight both as a control and as interaction term. We do not find that the coefficient on change in total assets becomes insignificant. Our paper complements the paper by Amel-Zadeh et al. (2013) by showing that the effect of the change in average risk weight on procyclicality depends on the types of banks and whether banks purchase or sell assets. Moreover, we point out additional drivers of procyclicality, which is important for understanding procyclicality. The findings are also interesting because they provide indirect evidence that for many banks the regulatory capital ratio does not seem to be binding as otherwise procyclicality could not arise independently of changes in average risk weights of a bank s assets. 5

7 Our paper also contributes to the literature on capital structure decisions of banks and the speed of adjustment to the optimal leverage and capital ratios (e.g., Gropp and Heider (2010) and Berger et al. (2008)). These papers include leverage as proxy for the systemic relevance of a bank and its likelihood of bailout (see, e.g., Berger et al. (2008)). Thus, a driver of the procyclical relation between size and leverage might be that the optimal leverage ratio is increasing in total assets due to a higher probability of bailout. However, this is unlikely to be the only driver of procyclicality. The remainder of this paper is organized as follows. We develop our hypotheses in Section 2. Section 3 presents the empirical methodology. Section 4 describes the data. Section 5 provides the results of our regression models. Section 6 concludes. 2 Hypotheses Our objective is to identify drivers of procyclicality. To do so we interact possible determinants of bank capital structure with changes in total assets ( Total Assets). For each determinant we distinguish between the direct effect on changes in leverage ( Leverage) and the indirect effect through procyclicality as measured by the interaction term. Unless regulatory capital constraints are binding, the static-trade off theory predicts that a bank s optimal leverage ratio is higher when the economy grows and the economic outlook is stable than when the economy shrinks and the economic outlook is uncertain. Thus, banks will increase their leverage if the economic outlook is good. Moreover, if banks use asset expansions to increase leverage, a given increase in total assets is associated with a higher increase in leverage if the economic outlook becomes more positive. We use growth in GDP ( GDP) and volatility ( VIX) as proxies for economic conditions and predict a positive respectively negative stand-alone effect of these variables on Leverage. In 6

8 addition, we predict a positive coefficient for the interaction of GDP with Total Assets and a negative coefficient for the interaction term of VIX. Regulatory capital constraints are less binding for banks with low leverage and high regulatory capital ratios. Consequently, such institutions can finance new loans or purchase additional financial assets with debt. Indeed, it may be optimal for these institutions to use debt financing to adjust leverage to its target level if current leverage is below target. In contrast, banks with high leverage and low regulatory capital ratios may use equity to finance balance sheet expansions and even sell assets to reduce their leverage (pay off debt). Therefore, we predict negative coefficients for (lagged) leverage and the interaction of leverage with Total Assets. For (lagged) total regulatory capital (tier capital ratio), we predict a positive coefficient for both the interaction term and the stand-alone variable. Regulatory capital constraints depend on a bank s average risk weight. If the average risk weight decreases, a bank can increase its leverage while holding its regulatory capital ratio constant. Amel-Zadeh et al. (2013) develop a model in which they show that if a bank s regulatory capital constraint is binding, procyclicality can only arise if the average risk weight decreases (increases) upon balance sheet expansions (contractions). Therefore, we interact changes in a bank s average risk weight ( Risk Weight) with Total Assets and introduce a dummy variable to capture differences between an increase and a decease in total assets. We predict a negative (positive) coefficient for the interaction term of Risk Weight if the asset base increases (decreases). A bank s leverage ratio also depends on the market value of its equity. We use the market-to-book ratio of equity to capture the relation between the bank s book and market equity. Other measures, such as the market-to-book ratio of total assets (Tobins Q) and the market leverage ratio are closely related given that the book value of debt is generally 7

9 used as a proxy for its market value. If the market-to-book ratio increases, banks may increase their leverage if they target a certain market leverage ratio. However, banks may also use a high market-to-book ratio to issue equity. Consequently, we predict positive coefficients for both the market-to-book ratio of equity and its interaction with Total Assets if banks use high market values of equity to increase debt, and negative coefficients if banks seize high market values to raise equity. Accounting has been blamed to contribute to procyclicality. Different accounting items have different implications for financial reporting and regulation. In this context, it is interesting to test the contribution of unrealized gains on AfS, realized gains/losses on AfS & HtM investments, realized gains on loans, and trading income to procyclical bank leverage. All four variables have a direct negative effect on Leverage as gains increase equity and thus reduce leverage. The effect on procyclicality is less clear. Unrealized gains on AfS increase equity, but not regulatory capital; the other three items increase regulatory capital. Banks might increase their leverage in response to gains that feed into regulatory capital. We therefore make the following predictions. First, the coefficients on all four stand-alone variables are negative. Second, if banks adjust their capital structure due to an increase in regulatory capital, we predict positive coefficients for the interaction terms of realized gains/losses on AfS & HtM, realized gains on loans as well as trading income. A positive coefficient on the interaction term of realized gains on loans has to be interpreted with care as it may be the case that proceeds from a sale of loans may be used to repay debt. In this case, there is a positive association between Total Assets (reduction of assets) and Leverage (reduction of leverage). To formally distinguish the case of an increase in assets from the case where assets are decreasing, we will perform a robustness check where we include a dummy variable that is positive if the change in total assets is negative. 8

10 3 Empirical Methodology This section describes the identification strategy we follow to test our hypotheses and defines the variables we employ in our empirical analysis. Table 1 provides a comprehensive list of all the variables used in this paper. We explore the cross-sectional and time-series dimensions of bank leverage via a panel regression analysis. As a first step, we investigate whether the leverage of US commercial and savings banks is procyclical. For that purpose, we estimate a regression model which is similar to the main model of Adrian and Shin (2010). In particular, the leverage growth of bank i in quarter t is given by Leverage i,t = α + α i + α t + β Total Assets i,t + γ Goodwill i,t + ɛ i,t (1) where α denotes the intercept, α i the bank-fixed effect, α t the quarter-year-fixed effect and ɛ i,t the vector of regression disturbances. The main coefficient of interest is β, which captures the relationship between changes in leverage and changes in total assets. If this coefficient is positive and significant, leverage is procyclical. We define leverage as the ratio of total book assets to total book equity. Since we are interested in the comovement between leverage and balance sheet size, we use a book definition for total assets. Leverage and Total Assets are given by ln[variable i,t ] - ln[variable i,t 1 ] as in Adrian and Shin (2010). Goodwill i,t controls for the extent to which mergers & acquisitions mechanically drive changes in leverage and total assets. It is defined as the fraction of [Goodwill i,t 9

11 - Goodwill i,t 1 ] to [Total Assets i,t - Total Assets i,t 1 ] 1. The above regression model is estimated by ordinary least squares and standard errors are adjusted for within-bank clusters (see Petersen (2009)). As explained in Section 2, Leverage is likely driven by macroeconomic fundamentals, lagged leverage, market values, regulation as well as accounting/profitability. To identify these effects econometrically, we extend regression model (1) such that the leverage growth of bank i in quarter t is given by Leverage i,t = α + α i + β Total Assets i,t + γ GDP t + δ VIX t (2) + ζ Leverage i,t 1 + η q i,t 1 + ζ Total Reg. Capital Ratio i,t 1 + η Risk Weight i,t + ι Accounting Items i,t + κ Goodwill i,t + ɛ i,t We employ GDP and VIX as macroeconomic variables (both defined as log differences of GDP and VIX respectively). The real US GDP 2 is an indicator for the overall economic condition and the implied stock market volatility, measured by the market volatility index (VIX) of the Chicago Board Options Exchange, proxies for the risk in the US economy. GDP and VIX are constant across banks within each quarter and therefore perfectly 1 In particular, if two banks merge or one bank takes over another bank, the balance sheet of the resulting entity will be larger than the balance sheet of the acquiror before the transaction. Depending on the leverage ratios and the relative size of the two banks, the book leverage of the combined bank will be larger or smaller. If leverage increases, the business combination mechanically causes a procyclical leverage pattern. We use the growth of a bank s recognized goodwill as an indicator for recent M&A activity since the goodwill of the combined/surviving entity typically increases strongly during a business combination (during a merger or acquisition, the residual of purchase price and book value of net assets is recognized as goodwill on the bank s balance sheet). Many of the smaller banks in our sample have zero goodwill recognized on their balance sheet. Consequently, a definition of Goodwill based on log differences results in non-defined/missing observations for these banks which reduces the number of observations in our regression analysis significantly. We use the above definition of Goodwill instead since this variable is defined/non-missing for most observations ([Total Assets i,t - Total Assets i,t 1 ] is typically non-zero) and economically very similar to the log definition. 2 Chained to For robustness, we also conducted our empirical analysis with the S&P500 index and nominal GDP instead of real GDP. This does not change the nature of our results. We decided to use real GDP as this variable captures actual economic activity most closely. 10

12 collinear with the quarter-year dummy. Since we are interested in the effect of changes in macroeconomic conditions on Leverage, we drop the quarter-year-fixed effect from the regression equation and keep the macro-variables. Leverage i,t 1 measures the leverage ratio at the beginning of the period. As discussed in Section 2, we investigate the impact of market values on Leverage by considering a bank s lagged market-to-book ratio of equity (denoted by q). The total regulatory capital ratio and Risk Weight (log difference) are variables that capture regulatory effects. The total regulatory capital ratio is a measure of the bank s capitalization. It is defined as the sum of tier 1 and tier 2 capital divided by riskweighted assets (RWA) 3. The (average) risk weight is given by the ratio of risk-weighted assets to total assets. We estimate the effect of accounting/profitability on leverage via the vector accounting items. This vector contains unrealized gains/losses on AfS securities, realized gains/losses from the sale of loans, realized gains/losses on AfS & HtM securities and trading income. To ensure that the accounting items are comparable across banks, we normalize these variables by total assets. Realized gains/losses occur when an asset is sold at a market price that exceeds/is lower than its carrying amount on the balance sheet. In this paper, we consider realized gains/losses on loans and realized gains/losses on AfS & HtM securities. Realized gains/losses on loans measure gains/losses on the sale of customer, commercial or mortgage loans. Realized gains/losses on AfS & HtM securities capture gains/losses on the sale of AfS and HtM securities. Realized gains/losses are recognized in the income statement and regulatory capital. In contrast, any unrealized and temporary change in the fair value of AfS securities is recognized as unrealized gain/loss in accumulated other comprehensive income in shareholders equity. These gains/losses neither impact the bank s income statement nor its regulatory capital. Trading income captures realized and unrealized gains/losses as well as fees from assets that are held in the 3 As defined by the Basel I and II accords of the Bank of International Settlements. 11

13 bank s trading account. Trading account assets are reported at their fair value and any change in fair value is directly recognized in the income statement and regulatory capital. To understand the drivers of procyclical bank leverage, we interact our regression variables with Total Assets and estimate the following regression model Leverage i,t = α + α i + β Total Assets i,t (3) + γ Total Assets i,t GDP t + δ Total Assets i,t VIX t + ζ Total Assets i,t Leverage i,t 1 + η Total Assets i,t q i,t 1 + θ Total Assets i,t Total Reg. Capital Ratio i,t 1 + ι Total Assets i,t Risk Weight i,t 1 Total Assets>0 + κ Total Assets i,t Risk Weight i,t 1 Total Assets 0 + λ Total Assets i,t Accounting Items i,t + µ Z i,t + ɛ i,t Each interaction term measures the relationship between the procyclical leverage pattern and the interacted variable. Based on our hypotheses from Section 2, we introduce two interaction terms for Risk Weight to properly estimate the potential non-linear relationship between this variable and procyclical leverage. The vector Z i,t contains the stand-alone values of the interacted variables as well as Goodwill i,t. 4 Data 4.1 Data Sources and Sample Selection We obtain our bank-level data from the bank fundamentals database of SNL Financial and the real GDP and volatiliy data (VIX index) from the homepages of the Bureau of 12

14 Economic Analysis and the Chicago Board Options Exchange (CBOE) respectively. SNL s bank database contains very detailed information about the balance sheet and income statement of all active, acquired/defunct and listed/non-listed US financial institutions that report to the SEC, the Federal Reserve System, the FDIC or the Comptroller of the Currency. In this paper, we focus on US commercial and savings banks. We retrieve data on the holding company level to avoid investigating certain instituions multiple times and to ensure a high data quality. Specifically, we investigate all US commercial and savings banks that file Y-9C and 10-Q reports 4. Our sample covers the time period from Q to Q To be included in our sample, we require that a bank has non-missing and positive values for total assets and total (book) equity as well as non-missing values for total assets growth and leverage growth. We eliminate outliers that are most likely not driven by the day-to-day business of a commercial or savings bank 6 by excluding the top and bottom 1% of observations based on total assets growth and leverage growth respectively 7. These selection criteria result in an initial sample of bank-quarter observations attributable 4 In the US, a bank holding company is defined as a company which has control over any bank or over any company that is or becomes a bank holding company (Bank Holding Company Act of 1956). All US bank holding companies are directly regulated and supervised by the Federal Reserve System and, in the case of total book assets exceeding $150 million ($500 million as of 2006), required to file a quarterly Y-9C report (Consolidated Financial Statements of Holding Companies). The Y-9C report is publicly made available by the Federal Reserve Bank of Chicago and includes a consolidated balance sheet, income statement, detailed supporting schedules and a schedule of off-balance sheet items. This additional layer of regulation ensures a high data quality and applies even though the constituent-entities of the bank holding company are already regulated by the FDIC or the Comptroller of the Currency. If the holding company has more than 300 shareholders, it is also required to register with the SEC and to file quarterly 10-Q and annual 10-K reports. 5 Broker-dealers that became a bank holding company during the financial crisis (e.g. Goldman Sachs, Morgan Stanley etc.) are not considered. Broker-dealers that were acquired by a commercial or savings bank are considered (there are very few such cases). 6 These outliers are typically the result of large mergers and acquisitions. By cutting the top/bottom 1% we do not eliminate the effects of medium-sized and small mergers and acquisitions. Therefore, we control for these business combinations by including Goowill i,t in our regression analysis (see Section 3). 7 We first cut by leverage growth and then by total assets growth. Our results do not change qualitatively if we first cut by total assets growth and subsequently by leverage growth. Using different exclusion thresholds also does not impact the nature of our results. 13

15 to 934 banks. Additionally focusing our attention to banks for which all regression variables (see Section 3) are non-missing reduces our sample to bank-quarter observations (800 institutions). 4.2 Descriptive Statistics Table 2 reports averages for key characteristics of our sample banks (full sample and by business model). The average balance sheet size of institutions in our sample is $11.34 billion. With average total assets of $1.92 billion, savings banks are smaller than commercial banks. Among commercial banks, those with more than 20% fair-value assets are significantly larger (average balance sheet of $22.87 billion). The leverage ratio of a typical bank in our sample is and thus lower than the leverage of the largest US investment banks, which is in the range of 20 to 35 (see for example Figure 16 in Adrian and Shin (2010)). Savings banks are less levered and better capitalized than commercial banks. The average risk weight of our sample banks is The asset structure of the observed institutions is typical for commercial and savings banks. Loans are the largest asset class and account for 65.85% of total bank assets on average. AfS securities constitute the second largest asset class (17.60%) and HtM securites cover only 3.81% of the balance sheets of our sample banks. Trading assets seem to play a minor role for most banks in our sample (0.21% of total assets). In fact, most savings banks as well as commercial banks with less than 20% fair-value assets have zero trading assets. Therefore, we will run our regressions from Section 3 without the variable trading income (stand-alone and interaction with Total Assets) for these institutions. The liability-side of the balance sheet reveals that deposits and senior debt are the two dominant sources of funding for US commercial and savings banks. 14

16 Table 3 shows summary statistics of all regression variables. Between Q and Q1-2013, US commercial and savings banks increased their balance sheet on average by 1.72% and their leverage ratio by 0.17% per quarter. Consistent with the asset structure of the banks, realized gains on loans (0.33 of total assets) and realized gains on AfS & HtM securities (0.05 ) are larger than trading income (0.02 ). Interestingly, unrealized gains/losses on AfS (0.03 ) tend to be smaller than realized gains/losses on loans or AfS & HtM. Savings banks tend to have a lower market-to-book ratio of equity (q i,t 1 ) than commercial banks. 5 Results Figure 1 plots Leverage and Total Assets for all bank-quarter observations of our sample and Figure 2 visualizes the same relationship for savings and commercial banks respectively. Each of the graphs shows a strong procyclical leverage pattern. Table 4 provides the estimation results for regression equations (1) and (2) for the full sample. The coefficient of Total Assets is positive and highly statistically significant across all regression models. capital structure as controls. We successively include additional determinants of bank The coefficients of nearly all of the variables exhibit the predicted sign and are highly statistically significant. Yet, the coefficient on Total Assets hardly changes. That is, the magnitude of the procyclical leverage pattern does not seem to be affected by the additional control variables 8. As predicted, the coefficients of GDP and 8 In untabulated results, we additionally interact Total Assets with a dummy variable that takes a value of one if Total Assets is negative and zero otherwise. The coefficient of this interaction term quantifies whether the procyclical leverage pattern is stronger or weaker for balance sheet contractions. We find that the estimate is negative but not statistically significant. 15

17 VIX are positive and negative respectively. In the full model only GDP is significant 9. Moreover, we find that leverage is decreasing when leverage is high and regulatory capital is low, which is consistent with our hypotheses from Section 2. Interestingly, banks reduce leverage when the market-to-book ratio of equity is high, which suggests that they raise equity when market values are high. The coefficient of Risk Weight is negative which suggests that banks reduce their leverage ratio when the average risk weight increases. The statistical significance of this variable increases in the full regression model. If we add Risk Weight as explanatory variable, the procyclical leverage pattern remains strong and the coefficient of Risk Weight is only weakly significant. In contrast, Amel-Zadeh et al. (2013) find that the procyclical leverage pattern vanishes when Risk Weight is added to the regression model (highly statistically significant negative coefficient). To test whether these different findings are due to differences in the empirical specification and/or sample selection, we replicate the regression setup of Amel-Zadeh et al. (2013) as closely as possible. In particular, we only consider commercial banks between Q and Q and employ identical sample selection criteria, data modifications, variable definitions and regression specifications. Our replicated sample consists of bank-quarter observations attributable to 390 commercial banks. In the replicated regression analysis we find that the coefficient of Total Assets decreases from to when we add Risk Weight as explanatory variable. However, the estimate of Total Assets remains highly statistically significant, which confirms our initial finding (the coefficient of Risk Weight is highly statistically significant as well). 9 The adjustment of leverage to the economic outlook might not only take place in the same but also in the subsequent quarter. As a robustness check, we therefore extend regression equation (2) by lagged macroeconomic variables. In untabulated results we find that the coefficients of both lagged and contemporaneous GDP are positive and highly statistically significant. 16

18 Unrealized gains of AfS securities, realized gains from loan sales, and realized gains on AfS & HtM securities all have highly significant and negative coefficients. Thus, banks do not immediately/entirely offset the positive effect of gains on equity by increasing their debt overproportionally. In the full model, the coefficient on trading assets turns positive but remains insignificant, which is probably due to the fact that trading assets play a minor role for our sample banks as reflected in Table As a robustness check, we estimate regression equation (2) with lagged accounting items (up to 2 quarters) and contemporaneous variables. We find that none of the lagged variables is significant. The negative contemporaneous coefficients of the accounting items remain highly significant. In terms of economic significance, the effects of Total Assets and unrealized gains AfS on Leverage are large. In particular, if the growth of total assets increases and unrealized gains on AfS decrease by one standard deviation, Leverage increases by 2.51 and 1.72 percentage points (pp) respectively relative to an unconditional mean of 0.17%. The effects of GDP (0.21 pp increase of Leverage in response to a one standard deviation increase in GDP), Risk Weight (-0.15 pp), realized gains on loans (-0.47 pp) and realized gains on AfS & HtM securities (-0.54 pp) are moderate. The coefficients of the remaining variables are economically small. Table 5 provides the estimation results of regression equation (2) for savings banks and commercial banks with less/more than 20% fair-value assets 11 respectively. We find strong procyclicality for all three types of banks. Indeed, the coefficient of Total Assets is significantly higher for savings banks than for both types of commercial banks. This is true despite the fact that most US savings banks are stock corporations that have access to public equity. The split by type of bank shows that the business models of these 10 This is also consistent with Laux and Leuz (2010). 11 The fraction of fair-value assets is given by the sum of trading assets and AfS securities divided by total assets. 17

19 institutions differ. In particular, leverage and gains are the only determinants of Leverage that remain statistically significant for all three types of banks. For savings banks all the other variables become insignificant. Despite the drop in significance of the other variables, the explanatory power of the savings banks model is very high (nearly 50%). For both types of commercial banks, GDP, leverage, and q remain significant. The only change in significance for both banks relates to the regulatory capital ratio and Risk Weight. The regulatory capital ratio is only significant for commercial banks with fair-value assets of less than 20%. In contrast, Risk Weight remains significant only for commercial banks with fair-value assets of more than 20%. The coefficient of trading income is negative and remains insignificant for commercial banks with fair-value assets of more than 20% since for these institutions trading assets still play a small role. However, another reason might be that these banks adjust their debt level to offset any direct effect of trading gains on Leverage. To test this possibility, we look at commercial banks with more than 30% or 40% of fair-value assets respectively. We find that the coefficient of trading income becomes more negative and statistically significant if we increase the fraction of fair-value assets (including trading assets), i.e. the immediate negative effect of profitable trading on leverage becomes stronger. To understand the drivers of procyclicality, we interact our regression variables with Total Assets. Table 6 provides the estimation results for regression equation (3) for the whole sample. The coefficient of the interaction term with GDP is positive and highly statistically significant. This confirms the intuition that procyclicality is strongly associated with the business cycle. We also find that procyclicality is lower for banks with a high leverage and a low regulatory capital ratio. In other words, these banks use less debt to finance asset expansions. The coefficient of the interaction term with Risk Weight is positive and strongly significant when total assets decrease. The pattern 18

20 is consistent with banks selling liquid assets with low risk weights to repay debt: The average risk weight increases while total assets and leverage both decrease. When total assets increase, the interaction term with Risk Weight is negative, as predicted, but not statistically significant. Of particular interest for the fair-value debate are the coefficients of the interaction terms with unrealized gains AfS, realized gains AfS & HtM and trading income, which are all not statistically significant. The coefficient of unrealized gains AfS is negative. This suggests that banks do not simultaneously increase their leverage ratio and asset base in response to pure accounting gains from AfS securities. Since AfS gains do not impact regulatory capital, this is in line with our hypothesis. The coefficients on the interactions of realized gains AfS & HtM and trading income are positive, which is also consistent with the regulatory capital channel discussed in Section 2. The coefficient on the interaction term of Total Assets with realized gains on the sale of loans is positive and highly statistically significant. The positive coefficient is consistent with two possible scenarios. First, banks use the proceeds from the sale of loans to repay debt (i.e., decreasing total assets and decreasing leverage). Second, banks that are active in the securitization of loans pursue an expansion strategy, i.e., they originate/purchase new loans financed with debt to subsequently repackage and sell these loans. To differentiate between the two explanations, we performed a robustness check and included a dummy variable that is one if the change in total assets is negative and zero otherwise. We find that the coefficient of this dummy variable is negative and statistically significant such that the first explanation seems unlikely. The effects of GDP and Risk Weight (asset contractions) on procyclical leverage (coefficient of Total Assets) are economically large. Specifically, an increase of GDP and Risk Weight by one standard deviation increases the procyclical leverage pattern by 5.49 and percentage points (pp) relative to an unconditional coefficient of 69.80%. 19

21 The economic magnitide of the interaction of realized gains on loans is moderate (2.26 pp). The coefficients of the other significant interaction terms are economically small. Table 7 provides the estimation results for the interaction terms for the three different types of banks. For savings banks, the only two variables for which the coefficient of the interaction term is significant are the market-to-book ratio and realized gains on loans. Both coefficients are positive. The difference between how savings and commercial banks react to an increase in their market-to-book ratio of equity is worth highlighting. For savings banks the coefficient on the interaction term with the market-to-book ratio is positive and statistically significant, but insignificant for commercial banks. In contrast, the stand-alone coefficient of the market-to-book ratio is not significant for savings banks, but significant and negative for commercial banks. Therefore, while commercial banks seem to raise equity when their market value increases, savings banks react more procyclically (i.e. lever up more via additional assets). One explanation might be that although savings banks have shares, issuing shares might be more expensive for the average savings bank than for the average commercial bank. The interactions with GDP and the leverage ratio are significant for both classes of commercial banks. An interesting difference arises with respect to the interaction of Total Assets with the regulatory capital ratio and Risk Weight. The interaction of the regulatory capital ratio is significant only for commercial banks with less than 20% fair-value assets. For commercial banks with more than 20% fair-value assets, the coefficient of Risk Weight for increasing total assets is negative and highly statistically significant (not significant for total sample or for other banks). Thus, commercial banks with more than 20% fair-value assets face higher procyclical expansions of their balance sheet if these expansions are accompanied by a decrease in the average risk weight. For asset contractions, the interaction of Total Assets with Risk Weight is positive and significant for both types of commercial banks. For commercial banks 20

22 with more than 20% of fair-value assets the evidence is consistent with the argument of Amel-Zadeh et al. (2013) that procyclicality is strongly linked to decreasing (increasing) average risk weights when banks that have a binding regulatory capital constraint increase (decrease) total assets. During the financial crisis of , the US govenment intervened in the asset and capital structure decisions of many commercial and savings banks in the form of asset relief programs (e.g. TARP), direct capital infusions and guarantees. It might be the case that these interventions had an impact on the drivers of procyclical leverage. As a robustness check, we therefore estimate regression equations (2) and (3) without the crisis period (Q to Q1-2009). In untabulated results we find that our insights from Section 5 are robust to excluding the financial crisis. Interestingly, the adjusted R 2 of all regression specifications is larger for the reduced sample period, i.e. the overall fit of the OLS models is better. This suggests that the crisis period is relatively more noisy than the non-crisis period. In Section 5 we argue that gains on loan sales are a key driver of procyclical bank leverage. The effect arises when total assets increase, which suggests that banks expanded their lending business through debt to securitize additional loans. In times of distress, banks contract their balance sheets such that the above effect should not be present during the financial crisis. We investigate the crisis period and find that this is indeed the case. It is important to note that in our paper as well as in the related literature (e.g., Adrian and Shin (2010), Adrian and Shin (2011) and Amel-Zadeh et al. (2013)) procyclical leverage measures how changes in asset growth relate to changes in leverage growth. This specification quantifies to what extent cyclical movements around the average growth of total assets lead to cyclical movements around the average growth of leverage. Although we find that an increase in asset growth is associated with an increase in leverage growth, it is not possible to conclude from this finding that a general trend in the growth of banks 21

23 is associated with a growth in leverage. On the contrary, as Figure 3 shows, the balance sheet of the average (equally-weighted) bank in the full sample increased by a factor of nearly three between 1990 and During the same time period, the average leverage ratio decreased from 14 to 10. This pattern also holds individually for savings banks as well as commercial banks with more, respectively less, than 20% of fair-value assets. 6 Conclusion We provide empirical evidence on the prevalence and determinants of leverage procyclicality for US commercial and savings banks in the period from Q to Q Understanding the determinants of procyclical bank leverage is important for the identification of possible problems and remedies that are as diverse as reporting, regulation, and management. Our findings do not suggest that marking-to-market is a main driver of leverage procyclicality. Instead, our findings are consistent with banks using an expansion of their business to also adjust their leverage and capital ratios towards their target levels, which gives rise to procyclicality. Bank leverage is strongly procyclical for both savings and commercial banks, even after controlling for a large set of economic and bank-specific determinants of leverage. When taking into account economic significance, gains on loan sales are a key driver of procyclical savings bank leverage. The effect arises mainly when total assets increase. For commercial banks, GDP growth has an economically strong effect on leverage procyclicality. Also, for commercial banks, there is an economically strong relation between procyclicality and an increase in average risk weights when total assets decrease. This finding suggests that when banks contract their balance sheet relative to the trend, the sale of liquid assets with low risk weights to repay debt is a first order determinant of 22

24 procyclical leverage. As for savings banks, gains on loan sales are economically important drivers of leverage procyclicality for commercial banks with less than 20% fair-value assets. In contrast, gains on loans are not significant for commercial banks with more than 20% of fair-value assets. Instead, for these banks, leverage procyclicality is significantly stronger if asset expansions go along with a decrease in the average risk weight. Therefore, an asset growth above the trend is accompanied by an investment in securities with low risk weights such as, e.g., asset backed securities, so that the bank s average risk weight decreases. The lower regulatory capital requirements (lower risk weight) of these assets allow the bank to increase leverage. However, it is also conceivable that higher leverage was chosen because banks perceived these assets to be of lower risk (than the average financial asset on the balance sheet). After all, the regulatory capital constraints were not binding for these institutions. 23

25 References Adrian, T. and Shin, H. S. (2010), Liquidity and Leverage, Journal of Financial Intermediation 19(3), Adrian, T. and Shin, H. S. (2011), Financial Intermediary Balance Sheet Management, Annual Review of Financial Economics 3, Adrian, T. and Shin, H. S. (2014), Procyclical Leverage and Value-at-Risk, Review of Financial Studies 27(2), Amel-Zadeh, A., Barth, M. E. and Landsman, W. R. (2013), Does Fair Value Accounting Contribute to Procyclical Leverage?, Working Paper. Berger, A., DeYoung, R., Flannery, M. J., Lee, D. and Öztekin, O. (2008), How Do Large Banking Organizations Manage Their Capital Ratios?, Journal of Financial Services Research 34(2), BIS (2009), The Role of Valuation and Leverage in Procyclicality, Committee on the Global Financial System (34). Brunnermeier, M. K. and Pedersen, L. H. (2009), Market Liquidity and Funding Liquidity, Review of Financial Studies 22(6), Danielsson, J., Shin, H. S. and Zigrand, J.-P. (2012), Procyclical Leverage and Endogenous Risk, Working Paper. Greenlaw, D., Hatzius, J., Kashyap, A. K. and Shin, H. S. (2008), Leveraged Losses: Lessons from the Mortgage Market Meltdown, US Monetary Policy Forum Report No. 2. Gropp, R. and Heider, F. (2010), The Determinants Of Bank Capital Structure, Review of Finance 14(4), IMF (2008), Chapter 3: Fair Value Accounting and Procyclicality, Global Financial Stability Report. Laux, C. and Leuz, C. (2010), Did Fair-Value Accounting Contribute to the Financial Crisis?, Journal of Economic Perspectives 24(1), Persaud, A. (2008), Regulation, Valuation and Systemic Liquidity, Banque de France, Financial Stability Review: Special Issue on Valuation (12). Petersen, M. A. (2009), Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches, Review of Financial Studies 22(1), Plantin, G., Sapra, H. and Shin, H. S. (2008), Fair Value Accounting and Financial Stability, Banque de France, Financial Stability Review: Special Issue on Valuation (12).

26 Tables and Figures Table 1: Definition of Regression Variables This table defines the variables used in our panel regression analysis and indicates their respective data source. Variable Definition Data Source Total Assetsi,t Book value of all assets recognized on the balance sheet of bank i at the end of quarter t SNL Financial Leveragei,t Total Assetsi,t / Total Book Equityi,t SNL Financial GDPt Real US gross domestic product at the end of quarter t Bureau of Econ. Analysis VIXt Market Volatility Index (VIX) at the end of quarter t CBOE qi,t Market Capitalizationi,t / Total Book Equity i,t SNL Financial RWAi,t Total risk-weighted assets of bank i at the end of quarter t SNL Financial Total Reg. Capital Ratioi,t Total tier 1 and tier 2 capital of bank i at the end of quarter t / RWAi,t SNL Financial Risk Weighti,t Total risk-weighted assets of bank i at the end of quarter t / Total Assetsi,t SNL Financial Goodwilli,t Excess of purchase price paid over value of net assets acquired of bank i at the end of quarter t SNL Financial Total Assetsi,t ln(total Assetsi,t) - ln(total Assetsi,t 1) SNL Financial Leveragei,t ln(leveragei,t) - ln(leveragei,t 1) SNL Financial GDPi,t ln(gdpt) - ln(gdpt 1) Bureau of Econ. Analysis VIXi,t ln(vixt) - ln(vixt 1) CBOE Risk Weighti,t ln(risk Weighti,t) - ln(risk Weighti,t 1) SNL Financial Goodwilli,t (Goodwilli,t - Goodwilli,t 1) / (Total Assetsi,t - Total Assetsi,t 1) SNL Financial Trading Incomei,t Realized & unrealized gains/losses from trading assets of bank i during quarter t / Total Assetsi,t SNL Financial Realized Gains Loansi,t Net gains on the sale of loans of bank i during quarter t / Total Assetsi,t SNL Financial Realized Gains AfS & HtMi,t Net gains on the sale of HtM and AfS securities of bank i during quarter t / Total Assetsi,t SNL Financial Unrealized Gains AfSi,t Change in net unrealised gain on AfS securities of bank i during quarter t / Total Assetsi,t SNL Financial 25

27 Table 2: Bank Characteristics This table reports averages for various bank characteristics from Q to Q by business model and for the full sample. Panel A reports asset-specific variables and Panel B lists variables which are related to the liabiliy-side of the banks balance sheets. In Panel A, all figures are normalized by total assets (except for total assets). In Panel B, all figures are normalized by total assets except for leverage, the tier 1 capital ratio and the total regulatory capital ratio. Other financial assets include cash, interbank deposits, reverse repurchase agreements and fed funds. Other liabilites include all liabilites that cannot be classified as deposits, senior debt or subordinated debt. The fraction of fair-value assets is given by the sum of trading assets and AfS securities divided by total assets. Bank fundamentals are obtained from SNL Financial. Full Sample Panel A: Assets Savings Banks Commercial Banks 20% FV-Assets Commercial Banks > 20% FV-Assets Trading Assets [%] Available-for-Sale [%] Held-to-Maturity [%] Loans [%] Other Financial Assets [%] Total Financial Assets [%] Risk-Weighted Assets [%] Total Assets (US$ Billion) Full Sample Panel B: Liabilities Savings Banks Commercial Banks 20% FV-Assets Commercial Banks > 20% FV-Assets Deposits [%] Senior Debt [%] Subordinated Debt [%] Other Liabilities [%] Total Liabilities [%] Leverage Tier 1 Capital Ratio [%] Total Reg. Capital Ratio [%]

28 Table 3: Descriptive Statistics of Regression Variables This table reports the (equally-weighted) descriptive statistics of the regression variables. We report the 25% quantile (Q 0.25 ), median, mean, 75% quantile (Q 0.75 ), standard deviation (SD) and the number of observations (N). Panel A provides the statistics of the macroeconomic variables. Panels B to E list the descriptive statistics of bank-related variables for the full sample, savings banks, commercial banks 20% fair-value assets and commercial banks > 20% fair-value assets. The fraction of fair-value assets is given by the sum of trading assets and AfS securities divided by total assets. GDP, VIX, Leverage, Total Assets, Risk Weight, Goodwill and the lagged total regulatory capital ratio are denoted in percent. Unrealized gains AfS, realized gains loans, realized gains AfS & HtM and trading income are given in per mil of total assets. Bank fundamentals are obtained from SNL Financial and macroeconomic variables are retrieved from the websites of the Bureau of Economic Analysis (US Department of Commerce) and the CBOE respectively. Q 0.25 Median Mean Q 0.75 SD N Panel A: Macroeconomic Variables GDP [%] VIX [%] Panel B: Full Sample Leverage [%] Total Assets [%] Risk Weight [%] Goodwill [%] Unrealized Gains AfS [ ] Realized Gains Loans [ ] Realized Gains AfS & HtM [ ] Trading Income [ ] Total Regulatory Capital Ratio t 1 [%] q t Leverage t Panel C: Savings Banks Leverage [%] Total Assets [%] Risk Weight [%] Goodwill [%] Unrealized Gains AfS [ ] Realized Gains Loans [ ] Realized Gains AfS & HtM [ ] Total Regulatory Capital Ratio t 1 [%] q t Leverage t Panel D: Commercial Banks 20% FV-Assets Leverage [%] Total Assets [%] Risk Weight [%] Goodwill [%] Unrealized Gains AfS [ ] Realized Gains Loans [ ] Realized Gains AfS & HtM [ ] Total Regulatory Capital Ratio t 1 [%] q t Leverage t Panel E: Commercial Banks > 20% FV-Assets Leverage [%] Total Assets [%] Risk Weight [%] Goodwill [%] Unrealized Gains AfS [ ] Realized Gains Loans [ ] Realized Gains AfS & HtM [ ] Trading Income [ ] Total Regulatory Capital Ratio t 1 [%] q t Leverage t

29 Figure 1: Procyclical Leverage of US Commercial and Savings Banks This scatter plot shows the positive and highly significant relationship between Leverage and Total Assets (procyclical leverage) of US commercial and savings banks between Q and Q (42670 bank-quarter observations). Leverage and Total Assets are defined as ln[variable t ] - ln[variable t 1 ] and the data is obtained from SNL Financial. 20% Full Sample 15% 10% Total Assets 5% 0% 5% 20% 10% 0% 10% 20% Leverage 28