The contribution of bank regulation and fair value accounting to procyclical leverage

This study addresses the question of whether commercial banks exhibit procyclical leverage and, if they do, the extent to which bank regulation and fair value accounting are contributing factors. Procyclical leverage is evidence of excessive asset purchases or sales by banks, which can have negative consequences to the financial system. Many academic researchers, policymakers, and other practitioners contend that fair value accounting contributes to excessive responses by banks to changes in asset prices and hence contributes to procyclical leverage.¹ However, this contention fails to consider that regulatory leverage requirements can contribute to banks’ procyclical responses. Our findings reveal that bank regulation explains procyclical leverage for banks relatively close to the regulatory leverage constraint and contributes to procyclical leverage for those that are not. We also find that fair value accounting does not contribute to procyclical leverage.

Studying whether commercial banks exhibit procyclical leverage and, if they do, the extent to which bank regulation and fair value accounting are contributing factors is important to helping policymakers determine how best to minimize the effects of shocks to financial asset prices on the macro economy. A provision of the Emergency Economic Stabilization Act of 2008 required the U.S. Securities and Exchange Commission to investigate the extent to which fair value accounting contributed to the collapse of financial asset prices and instability of the financial system during the 2008–2009 financial crisis. Underlying this requirement is the belief that fair value accounting was a major factor contributing to the crisis because it fueled excessive asset sales by banks.

To gain insight regarding the way bank regulation can contribute to procyclical leverage, we describe analytically actions commercial banks can take in response to economic gains and losses on their assets resulting from upturns and downturns in the economy. A bank’s regulatory leverage cannot exceed an amount set by the regulator. A key reason regulatory leverage differs from accounting leverage is that risk weights are applied to assets in determining the former but not the latter.² The analysis shows that, for banks with a binding regulatory leverage constraint, procyclical leverage can result when the weighted average regulatory risk weight of assets bought (sold) in response to increases (decreases) in asset values is less than the weighted average risk weight of the assets in its investment portfolio prior to the purchase (sale). That is, in the analysis, absent differences in regulatory risk weights across assets, leverage is not procyclical for such banks, and thus procyclical leverage is attributable to bank regulatory requirements. For banks without a binding regulatory leverage constraint, both fair value accounting and bank regulatory requirements can contribute to procyclical leverage.

Based on insights from the analysis, we design empirical tests to assess the extent to which bank regulatory leverage requirements contribute to procyclical leverage. Our empirical tests are based on quarterly financial statement and regulatory data for a large sample of U.S. commercial banks from 2001 to 2013. Following prior research, we first estimate the relation between change in leverage and change in assets and find that the relation is significantly positive, which indicates that leverage is procyclical. However, consistent with predictions from the analysis, for banks relatively close to the regulatory leverage constraint, this procyclical relation evaporates when the change in a bank’s weighted average regulatory risk weight is included in the estimating equation. For banks relatively far from the regulatory leverage constraint, change in a bank’s weighted average regulatory risk weight contributes to, but does not fully explain, procyclical leverage. We provide additional evidence that banks manage their regulatory leverage, thereby contributing to procyclical leverage, by showing that the positive relation between change in assets and change in leverage is greater for changes in assets with lower risk weights, particularly for banks relatively close to the regulatory leverage constraint.

We then design tests to examine the extent to which fair value accounting contributes to procyclical leverage. First, we extend the relation between change in leverage and change in assets by including a measure of the portion of comprehensive income attributable to fair value accounting, i.e., fair value comprehensive income. If fair value accounting contributes to procyclical leverage, we expect fair value comprehensive income is positively related to change in leverage. Not only do we fail to find a positive relation but we also find that the fair value comprehensive income measure has a negative relation with change in leverage as expected for any increase in equity. Second, we extend this relation by including the interaction of the measure and the bank’s net purchases of assets. If fair value accounting contributes to procyclical leverage, we expect the interaction is positively related to change in leverage. Contrary to this prediction, we find no evidence of a positive relation between fair value comprehensive income and banks’ net purchases of assets.

Third, we estimate the relation between change in leverage and change in assets, disaggregating change in assets into fair value comprehensive income, change in equity other than that arising from comprehensive income, change in debt, and other changes in assets. If fair value accounting contributes to procyclical leverage, we expect the relation between change in leverage and fair value comprehensive income is less negative than that between change in leverage and change in equity. Contrary to this prediction, we find that the relation is more negative than that between change in leverage and change in equity. Taken together, these findings reveal no evidence that fair value accounting contributes to procyclical leverage.

Because of the asymmetry in accounting for gains and losses under modified historical cost accounting and because the concerns about fair value accounting and procyclicality arose during the economic downturn that followed the financial crisis, we estimate the relations described above separately for quarters of economic upturns and downturns. Inferences based on these separate estimations are essentially the same as those for the combined sample. Most importantly, in upturns and downturns, there is no evidence of procyclical leverage for banks relatively close to the regulatory leverage constraint when the change in a bank’s weighted average risk weight is included in the estimating equation or that fair value accounting contributes to procyclical leverage.

We also test whether there is an association between fair value accounting and procyclical leverage for broker-dealers, which are not subject to risk-weighted regulatory leverage requirements but could maintain capital to meet an internally imposed value-at-risk criterion. Findings reveal a positive relation between change in leverage and change in assets, i.e., procyclical leverage, for broker-dealers, and there is no evidence that fair value accounting contributes to this relation.

The paper proceeds as follows. The next section provides a discussion of the institutional background and related research. Section 3 presents our analysis of how bank regulation and fair value accounting can contribute to procyclical leverage. Section 4 develops our empirical predictions and specifies our estimating equations. Section 5 describes the data and sample selection, and section 6 presents the empirical results. Section 7 concludes.

To gain insight regarding the way fair value accounting and bank regulation can contribute to procyclical leverage, we describe analytically actions commercial banks can take in response to economic gains and losses on their assets resulting from upturns and downturns in the economy. In doing so, we do not model equilibrium bank behavior. Rather, we design the analytical description to focus on how a binding regulatory leverage constraint can result in procyclical accounting leverage.⁶ Thus we characterize banks as maximizing leverage subject to a constraint on a regulatory leverage ratio, which is the reciprocal of the regulatory capital ratio. The regulatory leverage constraint could be that imposed by the regulator or one that builds in a buffer the bank views as an effective constraint. The analysis shows that, for a bank with a binding regulatory leverage constraint, procyclical leverage is attributable to bank regulatory leverage requirements and not fair value accounting. For a bank that does not face a binding regulatory leverage constraint, fair value accounting may contribute to procyclical leverage. Our empirical tests, developed in section 4, distinguish banks based on the proximity of their regulatory leverage to the externally imposed regulatory leverage constraint.

Our analytical description assumes that, similar to other entities, banks seek to maximize economic return on equity (Adrian and Shin 2010). Thus they use debt financing to acquire risky assets, which increases leverage.⁷ Although banks would seek to buy an unlimited amount of risky assets funded by debt, debt capital providers charge increasingly higher prices as debt increases because higher levels of debt are associated with a higher likelihood of financial distress. As a result, banks are limited in the amount of risky assets they can buy and cannot increase leverage indefinitely (Kraus and Litzenberger 1973). Unlike other entities, banks face an additional constraint on leverage that is imposed externally by the regulator. It is an empirical question whether the market or regulatory constraint is more binding.

There is no consensus in the finance literature as to whether there is an optimal capital structure (e.g., Modigliani and Miller 1958; Kraus and Litzenberger 1973; Myers 1984; Myers and Majluf 1984). Accordingly, we make no assumptions regarding the optimality of banks’ capital structures. However, Flannery and Rangan (2006) provide evidence that industrial firms have target capital structures and manage leverage ratios to achieve their targets. If banks manage to a target leverage level, then we assume they will take actions to maintain this level. That is, in the face of increasing (decreasing) asset values, banks likely will buy (sell) assets and issue (repay) debt in amounts sufficient to restore leverage to the level it was at before the increase (decrease) in asset values. However, if banks buy or sell assets to maintain a target leverage level, there would be no observed change in leverage and hence no reason to expect a relation between change in leverage and change in assets. Thus observing a positive relation between change in leverage and change in assets is evidence that banks do not manage accounting leverage to a targeted amount or do so with a lag.

A key reason regulatory leverage differs from accounting leverage is that risk weights are applied to assets in determining the former but not the latter. In particular, regulatory leverage can be smaller than accounting leverage if a bank invests in assets with risk weights less than one. Because regulatory leverage depends on the risk weights regulators assign to a bank’s assets, in striving to maximize return on equity, banks need to take into account the trade-off between buying (selling) assets with lower risk weights—and thus lower expected return per dollar of assets bought (sold)—and fewer assets with higher risk weights—and thus higher expected return per dollar of assets bought (sold).

To assess the effects on leverage of banks striving to achieve their assumed objective—i.e., buying or selling assets to maximize leverage subject to a regulatory leverage constraint—we proceed in two steps. First, we analyze how regulatory and accounting leverage change during the period if the bank does not buy or sell assets in response to the income it earns. Second, we derive how regulatory and accounting leverage change if the bank buys or sells assets to meet its assumed objective.

We analyze a bank for a single period, where t ₀ marks the beginning of the period and t ₁ the end. At t ₀ the bank has assets A ₀ > 0, equity capital K ₀ > 0, and debt D ₀ > 0, with A ₀ = K ₀ + D ₀. The bank’s leverage ratio is \( {L}_0=\frac{A_0}{K_0} \).⁸ For risk-based capital regulation, bank assets are assigned risk weights from a vector, V.⁹ We denote the bank’s weighted average risk weight at t ₀ as V ₀ ≥ 0, which results in a regulatory leverage ratio of \( {R}_0=\frac{V_0\times {A}_0}{K_0} \). Thus, in the analysis, if risk weights equal one for all assets, then accounting and regulatory leverage are the same, and hence ΔL = 0 when ΔR = 0.¹⁰

The purpose of our analytical description is to determine the circumstances under which it is possible for accounting leverage to be procyclical, i.e., ΔL > 0 in upturns and ΔL < 0 in downturns when banks manage regulatory leverage to maintain it at the regulatory constraint, i.e., ΔR = 0. The analytical description shows that ΔL > 0 (ΔL < 0) in upturns (downturns) when ΔR = 0 is possible only when assets are risk weighted in determining R but not in determining L and banks buy (sell) assets with risk-weights lower than the weighted average risk-weight of their existing assets. Procyclical leverage does not arise from including fair value accounting in the analysis.

For simplicity, our analysis does not distinguish between accounting equity and regulatory capital, i.e., the bank’s capital comprises only accounting equity. However, regulatory leverage is based on regulatory capital, which is accounting equity adjusted for items the regulator excludes from regulatory capital. For example, unrealized gains and losses on available-for-sale debt securities are not included in regulatory capital, and although unrealized losses of available-for-sale equity securities are included, 55% of unrealized gains are excluded. In addition, banks are subject to other regulatory leverage constraints, one that depends on a different measure of regulatory capital and another that depends on accounting assets rather than risk-weighted assets (Bens and Monahan 2008; Beatty and Liao 2014).¹¹ As described in section 4, our empirical tests include the effects of these unmodeled differences between regulatory leverage based on risk-weighted assets and that based on accounting assets.

Between t ₀ and t ₁ the economy can expand, contract, or remain unchanged. We denote positive (negative, zero) economic growth by a growth factor, g > 1 (0 < g < 1, g = 1). The bank earns income during the period, I ₁, that depends on the state of the economy, where I ₁ = (g – 1)A ₀.¹² Because our focus is on the potential relation between fair value accounting and procyclical leverage, in the analysis the bank’s only income comprises fair value gains or losses. I ₁ is positive if the economy expands and negative if the economy contracts. At t ₁ the bank has assets of A ₁ = gA ₀ and capital of K ₁ = K ₀ + I ₁.¹³ Because leverage at t ₁ and t ₀ differ, we assume the bank will buy or sell assets if the return on equity it achieves from taking such actions is higher than from not taking such actions. As shown below, subject to its regulatory leverage constraint, when the economy expands (contracts), i.e., g > 1 (g < 1), the bank has an incentive to buy (sell) assets. Without loss of generality, in the analysis regulatory risk weights remain constant throughout the economic cycle, i.e., they are independent of g.

When the bank does not buy or sell assets in response to the income it earns, changes in its regulatory and accounting leverage depend on the state of the economy, that is, on whether the bank has fair value gains or losses. In particular,

Eqs. (1) and (2) illustrate the mechanical relation between change in leverage and change in asset value. That is, regulatory and accounting leverage do not change, i.e., ΔR = 0 and ΔL = 0, where ΔR = R ₁ – R ₀ and ΔL = L ₁ – L ₀, if the economy exhibits no growth, i.e., g = 1. If the economy expands (contracts), i.e., g > 1 (g < 1), regulatory and accounting leverage decrease (increase), i.e., ΔR < 0 and ΔL < 0 (ΔR > 0 and ΔL > 0). Adrian and Shin (2010) make a similar observation that, in the absence of action taken by the bank, there is an inverse relation between the size of bank’s balance sheet and leverage.

When the bank buys or sells assets to achieve its objective of maximizing leverage to maximize return on equity, the bank takes steps to counteract the mechanical relation between fair value gains or losses and leverage. Because the bank seeks to maximize leverage, the bank finances its asset purchases with debt or uses proceeds from asset sales to repay debt. If d > 0 (d < 0) represents the amount of assets the bank buys (sells) to maintain its regulatory leverage ratio, R ₀, then assets in period one, A ₁, is the sum of gA ₀ and d, where d = ΔD = D ₁ – D ₀. To maintain its regulatory leverage at the regulatory constraint, i.e., ΔR = 0, the bank chooses d such that:

V ^* denotes the weighted average regulatory risk weight of assets bought or sold. Eq. (3) reveals that the amount of asset purchases (sales) during economic upturns (downturns) depends on growth in the economy, g, the bank’s initial leverage, L ₀, and the weighted average risk weight of the assets bought or sold relative to that of the bank’s initial assets, V ₀/V ^* .

Of key importance to our research question is that Eq. (3) reveals that, because L ₀ > 1, d > 0 (d < 0) when g > 1 (g < 1), procyclical leverage is possible only if the weighted average regulatory risk weight, V ^* , of assets bought or sold to achieve ΔR = 0, d, is less than the bank’s initial weighted average regulatory risk weight, V ₀, i.e., only if V ^*  < V ₀. Moreover, in the context of the analytical description, g > 1 (g < 1) implies that ΔL > 0 (ΔL < 0) if and only if V ₀/V ^*  > 1, i.e., V ^*  < V ₀.¹⁴ As a result, the existence of procyclical leverage does not arise because of fair value gains or losses.¹⁵

To show how procyclical leverage results if the weighted average regulatory risk weight of assets bought or sold is less than that of its initial assets, consider the following illustration relating to asset purchases. Assume a bank has 100 in assets with a risk weight of one, 80 in debt, and 20 in equity, which implies that its accounting and regulatory leverage are both five, and V ₀ = 1. Assume further that the bank’s assets increase in value by five to 105, and the risk weights of the assets do not change. Absent taking any action, the bank’s accounting and regulatory leverage both decrease to 4.2 (= 105 / 25). However, in its quest to maximize leverage, the bank buys 30 in assets by issuing 30 in debt. Because its regulatory leverage constraint is five, the mix of assets the bank buys is 10 with a risk weight of zero and 20 with a risk weight of one. Thus V ^*  = [(10 × 0) + (20 × 1)] / 30, which is less than V ₀ = 1. This action results in regulatory leverage of 5 (= [(125 × 1) + (10 × 0)] / 25) and leverage of 5.4 (= 135 / 25), which is procyclical. Other asset purchase combinations can achieve this goal.

As an illustration relating to asset sales, consider a bank that has 120 in assets, 100 (20) of which have a risk weight of one (zero), 100 in debt, and 20 in equity, implying that its leverage is six, regulatory leverage is five, and V ₀ = 0.83 = [(100 × 1) + (20 × 0)] / 120. Assume that the bank’s risky assets, i.e., those with a risk weight of one, decrease in value by 10 to 90. Absent taking any action, the bank’s accounting and regulatory leverage increase to 11 (= 110 / 10) and 9 (= [(90 × 1) + (20 × 0)] / 10). To achieve procyclical leverage while restoring regulatory leverage to five, the bank needs to sell 40 of its risky assets and more than 10 of its riskless assets. For example, if the bank sells 12 of its riskless assets in addition to the 40 risky assets, leverage decreases to 5.8 (= [(90–40) + (20–12)] / 10). Thus V ^*  = 0.77 (= [(40 × 1) + (12 × 0)] / 52), which is less than V ₀ = 0.83.¹⁶

An additional implication of Eq. (3) is that, if d is sufficiently positive (negative) in economic upturns (downturns) to result in procyclical leverage, then the extent to which leverage is procyclical is proportional to V ₀/V ^* . That is, assuming V ^*  < V ₀, the lower the weighted average risk weight of the assets a bank buys (sells) to maintain its regulatory leverage, i.e., ΔR = 0, during upturns (downturns), the higher (lower) is d and the greater is the increase (decrease) in L, i.e., the more leverage is procyclical. To illustrate why this is the case, suppose that during upturns the bank buys assets with one of four possible risk weights, V ₁, V ₂, V ₃, and V ₄. If V ₁ < V ₂ < V ₃ < V ₄, then the amount of assets the bank can buy and achieve ΔR = 0, d, is decreasing across the risk weight categories, i.e., d ₁ > d ₂ > d ₃ > d ₄. This in turn implies that ∆L ₁ > ∆L ₂ > ∆L ₃ > ∆L ₄, i.e., the extent to which leverage is procyclical is higher the lower is the risk weight category of the assets purchased.¹⁷ More generally, the bank can buy assets in all four risk weight categories. To the extent that a bank buys more assets in lower risk weight categories, the resulting V ^* is lower. Eq. (3) reveals the lower is V ^* , the more assets the bank can buy, i.e., the larger is d, which in turn results in a larger increase in L, i.e., the more leverage is procyclical.

Although the above discussion explains how procyclical leverage can occur, it does not consider why a bank would find it beneficial to buy or sell assets with a weighted average risk weight less than that of its initial assets. To gain insight into this question, assume a bank can buy and sell a risky asset with a risk weight of one and a riskless asset with a risk weight of zero. When the bank experiences a gain and buys assets, it will buy as much of the risky asset as the regulator allows. In addition, the bank will buy as much of the riskless asset as possible, conditional on the marginal cost of debt, because even riskless assets have a positive return, which increases the bank’s return on equity.¹⁸ When the bank experiences a loss and sells assets, it will sell as little of the risky asset as the regulator allows. In addition, the bank will sell as much of the riskless asset as necessary to lower the marginal cost of debt to an acceptable level. For leverage to be procyclical, the bank needs to buy or sell enough riskless assets such that V ^* is less than V ₀, i.e., the weighted average risk weight before the asset purchases or sales.¹⁹

Plantin et al. (2008) show that, when there is illiquidity in financial asset markets, contagion can result, whereby the price of a financial asset is sensitive to the decisions of other financial institutions. For example, during economic downturns, fundamental values decrease, but there are negative externalities generated by other banks selling assets. When other banks sell a financial asset, its price is lower than its fundamental value, thereby exerting a negative effect on other banks, especially those that hold the asset. Anticipating this negative effect, the bank may attempt to preempt the price decrease by selling the asset it holds. However, such preemptive action amplifies the price decline. Thus, during an economic downturn, fair value accounting amplifies asset price declines relative to changes in fundamental value.²⁰

Based on the analysis in section 3, we design tests to assess the extent to which bank regulatory leverage requirements contribute to procyclical leverage. We then design tests to examine the extent to which fair value accounting contributes to procyclical leverage. Finally, we examine whether inferences we draw from these tests apply in both economic upturns and downturns.

We obtain quarterly financial statement data from the Compustat Bank files (three-digit SIC 602) and the WRDS Bank Regulatory Database, which includes accounting and regulatory data from regulatory forms filed with the Federal Reserve System, Federal Deposit Insurance Corporation, and the Comptroller of the Currency, from the first quarter of 2001 to the fourth quarter of 2013. Our sample period begins in 2001 because that is when data are available on other comprehensive income, which we require for estimating Eqs. (7) through (11).³¹ The sample comprises U.S. commercial banks and bank holding companies that file Call Reports and Federal Reserve Y-9C reports.³² We require all sample banks to have Tier 1 (total) regulatory leverage less than or equal to 25 (12.5) to exclude banks that are in violation of regulatory leverage requirements in effect during our sample period. We also exclude bank-quarter observations for banks that acquired other banks during the quarter with total assets greater than 10% of the acquiring bank’s assets to mitigate the effect of bank acquisitions on the bank’s change in assets (Collins and Hribar 2002). All sample banks have nonnegative values for total assets and equity in all quarters of the sample period. We winsorize all continuous regression variables at the 1% and 99% levels.³³ The final sample consists of 19,725 bank-quarter observations of 764 commercial banks. The appendix provides definitions for all variables.

Table 1, panels A and B, presents distributional statistics and correlations for the regression variables. Panel A reveals that the mean and median percentage change in leverage, ΔL, are 0.20% and −0.10%. The mean and median percentage change in assets, ΔA, 2.11% and 1.44%, largely are attributable to change in debt (mean and median ΔD = 1.92% and 1.28%). Untabulated statistics reveal that, on average, assets measured at fair value comprise 17% of total assets and 188% of equity, and fair value gains and losses comprise 3% of net interest revenue. Additional untabulated statistics reveal that change in weighted average regulatory risk weight, ΔV, arises from changes in loans and held-to-maturity, available-for-sale, and trading securities. In particular, the increase(s) in loans (held-to-maturity, available-for-sale, and trading securities) is (are) significantly associated with increases (decreases) in V. Panel A also reveals that ΔV arises from changes in risk weights within each asset class.

Table 1, panel B, reveals that ΔL is positively correlated with ΔA (Spearman and Pearson correlations = 0.48 and 0.21), which is consistent with procyclical leverage. However, the Spearman (Pearson) correlation between ΔL and fair value comprehensive income, FVCI, is negative, −0.20 (−0.10), which is inconsistent with fair value accounting being a source of procyclical leverage. In addition, consistent with predictions, the correlation between ΔL and change in weighted average regulatory risk weight, ΔV, is negative (Spearman and Pearson correlations = −0.29 and −0.21). All of these correlations are significantly different from zero.

This study addresses the question of whether commercial banks exhibit procyclical leverage and, if they do, the extent to which bank regulation and fair value accounting contribute. We describe analytically actions banks can take in response to economic gains and losses on their assets resulting from economic upturns and downturns. The analysis shows that, for banks with a binding regulatory leverage constraint, absent differences in regulatory risk weights across assets, procyclical leverage does not occur. For banks without a binding regulatory leverage constraint, fair value accounting and bank regulatory requirements both can contribute to procyclical leverage.

Based on insights from the analytical description, we design empirical tests to assess the extent to which bank regulatory leverage requirements contribute to procyclical leverage. First, we estimate the relation between change in leverage and change in assets and find that the relation is significantly positive, which indicates that leverage is procyclical. However, consistent with predictions from the analysis, for banks relatively close to the regulatory leverage constraint, this procyclical relation evaporates when the change in a bank’s weighted average regulatory risk weight is included in the estimating equation. For banks relatively far from the regulatory leverage constraint, change in a bank’s weighted average regulatory risk weight contributes to but does not fully explain procyclical leverage. We provide additional evidence that banks manage their regulatory leverage, thereby contributing to procyclical leverage, by showing that the positive relation between change in assets and change in leverage is greater for changes in assets with lower risk weights, particularly for banks relatively close to the regulatory leverage constraint.

Second, we design three tests to examine the extent to which fair value accounting contributes to procyclical leverage. First, we extend the relation between change in leverage and change in assets by including a measure of fair value comprehensive income and find that fair value comprehensive income has a negative relation with change in leverage as expected for any increase in equity. Second, we extend the relation by including the interaction between the measure of fair value comprehensive income and the banks’ net purchases of assets and find no evidence of a positive relation between fair value comprehensive income and the banks’ net purchases of assets. Third, we estimate the relation between change in leverage and change in assets, disaggregating change in assets into fair value comprehensive income, change in equity other than that arising from comprehensive income, change in debt, and other changes in assets and find that the relation between change in leverage and fair value comprehensive income is even more negative than that between change in leverage and change in equity. Taken together, these findings provide no evidence that fair value accounting contributes to procyclical leverage. Inferences relating to the extent to which bank regulation and fair value accounting contribute to procyclical leverage based on separate estimations using quarters of economic upturns and downturns are the same as those for the combined sample.

Taken together, the findings reveal that bank regulation contributes to procyclical leverage—particularly banks that are relatively close to the regulatory leverage constraint—but fair value accounting does not. These findings should be helpful to policymakers as they consider how best to minimize the effects of shocks to financial asset prices on the macro economy.